I'd seriously suggest against soldering your cartridge into the NES. It just doesn't make sense to do, and will likely not increase your NES's reliability if it's only having the occasional issue. Point to point soldered connections are always more problematic in the long run, and when it does wind up breaking (and with wires lap-soldered onto 72 x 2 pads, it WILL happen, no matter how clean you make it) you will be very very upset when you have to debug the thing. Believe me when I say this: I did this one time, though with a Game Genie, not a Power Pak. And never again. It was a huge mess, and I'm quite a skilled solder-er.
Bus errors are the number one cause of freezes, and they can be caused by two things: a faulty connection on the 72-pin connector but also by code problems. If you have a tight new 72 pin connector and clean cartridge contacts and are still getting occasional lockups when the unit isn't being bumped then it's possible the lockups are being caused by timing issues on the bus, which can be caused by a wide array of things. The Powerpak is not bulletproof, sometimes the mapper simulations are off by just enough that code which is especially picky may slip up. Of course, NTRQ, Pulsar, and PR8 are also not 100% free of bugs, which I'm sure Neil will agree with. So don't rule those possibilities out.