Use an inverted brass flat head machine screw. These will solder easily and depending the mechanical strength you want the part can be selected from a range with various head sizes.
Some possible candidate machine screws would be these part numbers from McMaster-Carr.
Length of 6mm
99658A524 M3 $9.68/100
96686A150 M2 $10.58/50
96686A210 M3 $7.94/50
Lower Cost with length of 6.35mm
92451A092 #3-48 $4.21/100
92451A106 #4-40 $4.29/100
92451A124 #5-40 $5.27/100
92451A144 #6-32 $5.90/100
92480A106 #4-40 $4.72/100
92480A144 #6-32 $5.85/100
This would certainly meet your criteria of being inexpensive, widely available, conductive and NOT through-hole. See the search page here.
Sticky residue is normally the flux. IPA doesn't dissolve flux, it just makes it runny. So if you gently wipe it off, all you are doing is smearing flux everywhere. Once the IPA evaporates, the flux turns into a horrible sticky mess.
The solution is to add a bit more IPA to the board, wait a minute or so for it to soften the flux, and then using something like kitchen roll, wipe in small circles, changing which bit of the kitchen roll you are using as you do (so that you don't smear what's already been wiped up back onto the board).
For intricate places around ICs, you can use the same process, but rather than wiping the kitchen roll on the board, use something like a pair of tweezers to push the roll down on the board and move back and forth around and between pins.
You should find the areas that have cleaned well stop being tacky. If you find anywhere that is still a bit sticky, then simply repeat the process.
What is also worth doing before you start cleaning with IPA is to gently chip off any really large blobs of flux - you can usually do this with a blunt instrument and as long as you aren't jamming something into the board it won't do any damage to the solder mask. The advantage of this is it means less flux on the board that has to be wiped off after it has softened up, so less that will smear around everywhere.
I've used OSH Park before, and never had an issue getting the boards clean with IPA and some elbow grease. As to why your particular board is being more stubborn to clean, it happens from time to time. Maybe you had ended up with more flux on the board, or when you were wiping off the IPA you used something that wasn't doing as good of a job of absorbing the grot. Could be many factors.
Best Answer
This looks like they used clear solder mask. If there was no solder mask, the gold would have plated all over the copper.
Your photo is not clear enough to confirm that, but try looking closely at an oblique angle and see if you can see a small gap between a gold-plated pad and a clear shiny layer on the board.