screen flashes occasionally with what appears to be ingame rendered stuff

some companies optimize their PAL releases so that the game will run at the same speed as their NTSC counterpart. Some game companies do not do this and the games will play 20% slower and with border on PAL. there are some lists on net for PAL optimized N64 games. for example this:

http://s9.zetaboards.com/Nintendo_64_Forever/topic/420230/1/

as an example let's look at Super Mario 64 PAL. this game will run 20% slower because of 50 hz/60 hz difference and will have a border because of 480i/576i difference. This is the case whether it's run on NTSC console or PAL console, with Everdrive or with original cartridge. it will be slow unless you hack the rom with PALadin which isn't recommended much because it might break audio. if you hack the rom to run at 60 hz, it will run at normal speed and without borders.

to keep things short what to do to play games at normal (intended) speed:

1)Use NTSC console and NTSC cartridges. it will output NTSC60 video via composite which nearly every tv should display fine.
2)Use NTSC roms on your everdrive. do not hack PAL roms to run in 60 hz unless you have to.
3)Use PAL cartridges when the game is PAL optimized. Even at this case i recommend NTSC cartridges, because optimization mighıt not be full. for example game is at normal speed, but still has a border etc.

there is no simple way to put your original PAL cartridges to a N64 and play it at 60 hz.