An indirect answer to your question.
We have done 0.5mm pitch LQFP DIY boards.
We used 'proper' laser printable PCB Artwork Drafting film
We spent quite a lot of time calibrating the exposure time of the PCB in the UV box, and IIRC it was sensitive to a +/- 5 second variation. Too short or too long produced poor results. IIRC, we made a 'PCB' with some test patterns for different track/space distances to help us calibrate things.
We still had quite a lot of trouble getting good results. Then we discovered that the laser printer was stepping in, and trying to produce a 'grayscale' when the PCB artwork 'pixel' boundaries didn't match its own idea of pixel boundaries. When we examined the artwork under a microscope, we could see that edges were defined by a fuzzy (dithered) half-tone pattern, rather than a much denser, more uniform edge.
We improved the results by 'fiddling around' with printer settings.
Then I redid the footprint of the 0.5mm pitch LQFP part so that the gap between pads was slightly bigger. That gave better results.
Edit:
I know folks who have tried a 1,700GBP 'ebay' PCB mill. AFAIK they gave up due to difficulties getting consistent results. They have now spent a lot more to get a proper LPKF milling machine.
Edit2:
Is the entire board 'packed', with a need for 0.25mm track/space everywhere or is it mainly around the 80pin part?
Depending on where you are in your development process, and the sort of issues you are needing to fix, a way to reduce the pain might be to make a 'breakout' board for the LQFP part with your high-quality manufacturer. That would have lead-time, but once you have some, you might be able to turn-round the rest of the PCB using DIY.
It may also be the breakout PCB can solve some of your layout issues. If you put it's decoupling capacitors etc on its breakout PCB, its behaviour might be okay. My experience is manufactured vias are much smaller than DIY vias freeing up board area. Further, putting vias under the chip are awkward to do on a DIY PCB. So you might get a lot of benefit from the manufactured breakout, and hence make the remaining DIY PCB easier to route.
A traditional breakout usually has pins on 0.1" centres, in a square around the chip. You don't need to do that. You could use finer pitch connections and with pins in a non-rectangular, convenient, shape for your problem.
Maybe even consider doing a 4-layer breakout PCB, to make the rest of the board as simple to layout and make as practical.
I did a co-op at a company where I had to design a PCB. This company used Atlassian JIRA, an issue tracker used primarily by software engineers. However, I also used it to track my physical board requirements and such. It integrates with Github or BitBucket, both of which provide version control.
I would say your needs also depend on how many people are involved. JIRA is suitable if you have an entire team working on a project. If it's just you, someone else on the team, and the clients, then I would suggest Github or Bitbucket alone. At the very least, version control allows you to upload your requirements, schematics, or gerbers, update them, and track them. Everything would be shared amongst you and the client. It is definitely more efficient than emailing back and forth.
If you are not familiar with version control, I recommend a google search on what version control is, and also how to use version control with hardware projects. Good luck!
Best Answer
Querying Google for "PCB Design Service" yields lots of offers, but obviously, you don't just feed them with the circuit but also with (probably a lot of) money. PCB design cannot be fully automated and will be done by humans.
I can recommend KiCad. This software can also work together with online autorouters (which is what you might be looking for) such as http://www.freerouting.net/, but beware that this no "circuit in, PCB out" magic machine. Unless you have a really high number of signals, the effort usesd in correctly configuring the autorouter to produce an acceptable result is much higher than routing by hand. Also you still have to place the parts, which is sometimes the hardest part.