Yes, there is a potential risk of bottle bombs, as with any incomplete ferment. The residual fermentables can be fermented by the remaining yeast in the bottle along with the priming sugar and produce more CO2 than intended. Ideally you should cold crash only after you are sure primary is complete. Many brewers simply leave the beer in primary for at least 2 weeks, which pretty much guarantees completion, (assuming a fairly stable or slightly increasing temperature.)
If you're unsure about primary being complete, you can try a forced ferment, to determine what the FG should be.
I'm not surprised conditioning at 60°F didn't produce much carbonation - the yeast need a fair activity level for the beer to carbonate. There is relatively little yeast in the beer during bottling - less than 100,000 cells/ml, which is typically less than 2% of that which was available during primary. With the low cell count and low temperature the yeast will not be very active at all. Better to condition for a week at 68-70*F before cold crashing to serving temps. During that time the yeast will ferment the priming sugar, produce the CO2 which then will dissolve into the beer over an additional week - faster if the beer is then kept cold.
Keeping the temperature low during bottle conditioning during the first week, is nowhere near as important as temperature management during the primary ferment, and sounds like for you it's causing more problems than it's solving.