One way which works well, is to use a different soldering technique. I use a small 'toaster oven' (cost about 20GBP) solder paste in a syringe, and a lighted magnifying glass. I also have a multi-meter with a temperature probe to monitor the process, but in reality a small torch, shone into the oven gives very good feedback. Look for all the solder paste to 'go shiny', and its done.
The toaster oven needs to be at least 1.3kW. Folks I know have failed with attempts to use a less powerful toaster oven. Other people use an 'electric skillet', or pizza oven with very good results.
Apply the solder paste in a very thin line across the PCB pads for the QFP, place the chip, and bake it in the oven. Providing there is very little excess solder, capillary action 'sucks' the solder under the pads, and there is very little bridging to clean up. Use fine (e.g. 1mm or narrower) to remove solder bridges between pins. We have done LQFP64, 0.5mm pitch, this way.
We mostly use manufactured PCBs, but people have used this successfully on DIY FR4 PCBs.
There are a lot of videos on the details of the process. Maybe start at Sparkfun, which had some videos.
A couple of techniques which improve the success rate are:
- Use a fine 'needle' on the syringe. When the hole is fine, it is much
less likely you'll apply too much solder. Several vendors sell
which can be cut to make a hole to suit the job.
- Don't panic about making solder bridges. Fine solder braid removes it
I'll add, this technique was taught to me by a local (UK, West Midlands) Secondary School teacher. He started teaching Surface Mount Technology soldering to 13yo's. They had much higher success rate than through hole parts, which tend to have more difficult to diagnose failure modes. Also, the students found it quicker to build boards; with three toaster ovens a class of 24 could all build a board in less than two hours. They are not using such fine technology as QFP though, typically small PIC's.