Been there, done this too many times to count.
Here are my suggestions.
1. Use either the wirewrap or enameled wire. The enameled wire will be easier to solder to and less likely to break where you have stripped off the insulation. Yeah, watch the fumes (toluene di-isocyanate fumes can sensitize you)
2. Pre-cut your wires to a suitable length to allow you to have the pcb flat and the device at 90' to the board.
3. Solder the wires to your IC's first row, standing straight up. When a row is done, bend each wire through 90' and solder these to your BOB* pcb. Use fine tweezers and a fine pick to comb the wires semi straight.
4. Repeat many times, you will find that this is how the picture from Prime was completed.
5. You will find that the enamelled wire is surprisingly flexible, until you have a lot of wires attached.
*break out board
Take your time and all will be OK. I do this on a semi regular basis and have always had excellent results.
Don't forget to use plenty of flux and clean it thoroughly afterwards with flux remover spray. Just be sure that the cleaner won't attack your wire !!!
After testing, epoxy encapsulate the works. 5 minute Araldite works well. Hot melt glue just doesn't cut it.
Be aware that there may be signal integrity issues at high speed..
FYI, 20 odd years ago I needed a way to convert a 84pin PLCC into a PLCC plug. I used a dremel with a diamond burr to grind away the encapsulation down to the lead in wires, removed the silicon die/bond wires and soldered pin by pin from the chip to break out board. Afterwards, I bound the flying lead wires together and epoxy encapsulated the lot. It worked 1st time (and probably is STILL to this day)
OSHpark design rules for the 4 layer boards are 5/5mil trace/space and drill holes to 0.011".
You should be able to make the board well within those rules.
It's not readily apparent on the web site. I've yet to find another manufacturer to match price and quality.
I've had them make me boards that adapt 80 pin QFP (0.4mm) to 84pin PLCC, rotated through 90'.
A pain to solder in, but nothing is available for this application.