Honestly, I wouldn't try to solder my own BGA's. I know this doesn't directly address your issues, but hear me out.
It takes a lot of work and effort to solder a BGA. There's a lot of trial and error. A lot of messed up test boards. But then it's soldered. Now what?
Now you have to prove that it's soldered correctly. For that you need one or more of the following: JTAG test (US$10k, never has 100% coverage), optical inspection (US$20k for the equipment), or X-Rays (US$500k). The cost of doing these tests is too much for the normal hobbyist, and is even beyond many small companies.
Skipping those tests, you proceed with debugging your PCB. And let's say that the BGA is a complex CPU. Inevitably you'll find a bug. The CPU will randomly crash. Is it your software, your electrical design, or the soldering on the BGA that's causing the problem? Debugging this, in light of some possibly problematic soldering, is going to be terrible. It will add a lot of time to your debug process, possibly months, and you'll loose a lot of hair on your head. And then you can repeat this for the next major bug.
Without confidence that your soldering is perfect, you will always have this dark cloud over your head. Every little bug that shows up "could be a BGA soldering problem". This is made worse if you have multiple engineers working on the same PCB since the software guy will be questioning the hardware guy, etc.
Then, even if the BGA soldering is perfect, did the chip get too hot? Did you destroy the chip by getting it too hot? Even on modern assembly lines this is an issue. But with the proper equipment you can adjust and measure the temperature profiles to at least get you in the right ballpark. On one board I did recently, the BGA's were being damaged. The solder balls looked great, but under a very nice X-Ray machine we could see that the gold bond wires melted from the heat.
I've been there. Not at the hobbiest level, but professionally as we were bringing up new boards while the assembly shop was learning to do BGA's. We had no JTag. No optical inspection. And the X-Rays were terrible. Our PCB had 11 BGA's on them. That was 2 years of hell I don't wish to repeat.
So, here's my recommendation:
Get someone who has the proper equipment, training, and experience to solder your BGA's. There are a lot of contract manufacturers that'll do a single BGA. It takes money, but that's way less than the time you'll spend trying to debug your own soldering.
If you must do it yourself, then you should get the proper equipment, training, and figure out how to get the experience required. For this to pay off in the end, you need to have a large enough company and need to justify the huge amount of time and money that you'll put into this.
But I would never try to just kludge something together. That's a recipe for, um, bad stuff.
What's your work environment? Mentioning toner transfer makes me think you're a hobbyist (which is fine), but as a hobbyist you're doing this because it's fun. Your time takes on a different value, and your budget outlook is quite different.
As a professional, I build circuit boards because it makes money for my employer. I'm paid fairly well, and it's not economically sensible for me to mess around with toner transfer and trying to solder to that board. I take my time and try to do it right the first time, send the boards out for manufacture, and move on to other projects. When the boards get back, I send them through the reflow oven or have a tech solder them up (the former is easier with soldermask, the latter is easier with silkscreen and soldermask) and test. If it works, great! If it doesn't, I revise the board accordingly and try again. Usually, the board works the first time, but if not, I revise it and send it out again.
Making a toner transfer board (or, at my workplace, a board cut out with a PCB router) is valuable when there's a major time crunch and you'd rather spend extra time to make sure that your prototype for the prototype works, rather than counting on the real prototype working the first time. I'm not going to sell or mass-manufacture routed boards, and they're laid out fundamentally differently than professionally made boards:
- Vias are free on professional boards, and difficult, large, and time-consuming on self-made boards
- Soldering is much more difficult. Keepaways, plane spacing, and thermals all behave very differently without soldermask. I'll work to make soldering easy on a self-made board, but lay out a professional board differently.
- Trace/space is smaller on a professional board. This could lead to major layout differences on some boards. Especially with high-frequency signals, moving things closer together can change impedances and cause problems.
- Some parts simply can't be soldered effectively on toner-transfer boards. 144-pin QFPs, QFN and BGA parts, and other tight layouts are far, far easier with soldermask.
In most cases, it's a better investment to send out for a few samples of the final product and wait for shipping than to do a toner transfer board as a prototype. If you enjoy doing toner transfer stuff, enjoy getting better at soldering, and your time isn't a part of your budget (hint: It isn't, even if you're a hobbyist - you have limited time too), then toner transfer makes some sense. If not, just get the real thing.
Best Answer
From my experience, one-off assembly is extremely expensive in the US. Most places would not even bother giving me a quote for a single piece. Furthermore, you're likely to have the same problem with building a breakout board, since that will have to be assembled (it just displaces the problem). However, I have found that (with some work), it is possible to do BGA parts if you have access to a reflow oven, or if you have access to a fairly good heat-gun.
For heat gun instructions: http://devbisme.webfactional.com/blogs/devbisme/2012/08/24/mounting-bga-pcb-quickly-and-cheaply
For a reflow oven: I used #186 rosin flux at 295 C for 90 seconds with a 200 C preheat (180 seconds). This is higher than most manufacturers recommend, but the oven I have access to was donated to the University and is from the early 90s, so it doesn't actually get that hot. It was not necessary for me to use a stencil or even apply any solder paste, I simply coated the footprint area with flux and carefully aligned the package to the silkscreen.
One bit of layout advice if you do not have access to an oven is to make the board as small as possible. This makes it possible to heat up the entire board to a consistent temperature.
Also remember to tent vias under the BGA, if you do not, capillary action will cause the solder to flow from the balls into the vias, which is not what you want to do. http://siliconexposed.blogspot.com/2012/07/bga-process-notes.html
Finally, if you don't have access to x-ray inspection, make sure your silkscreen outline is precise. It should be slightly bigger than the package to assist you in aligning the part. You can print out the silkscreen layer in Eagle on a conventional laser printer with 1:1 scale to make sure you can align it on paper first.