Conversions... what's the problem?

About that short crank solution, quite honestly I don't know how a mere 5mm shorter would make a huge difference in preventing pedal strike, I mean 5mm, that's pretty short.

I'd have though it come down to the choice of pedal than the crank length itself, a short clipless pedal would have less chance of a pedal strike than a wide BMX-style pedal.

My fixed machine is a conversion with 170mm cranks and is old enough to use a 120 rear spacing. Pedal strike has never been an issue either with track pedals or clipless as the BB is fairly high. BMX pedals could cause a few issues but I've never tried them. It all depends on the frame design itself and the Q distance (distance between pedals) made up of your BB width and crank profile. My tourer on the other hand would have awful pedal strike due to the low BB and would therefore be totally unsuited to fixed wheel shananigans.

One advantage of running an old road frame is often they have bottle cage braze-ons and readily accept brakes which is a god send IMO.