Nice one, Paul. Those heat-wraps should be plenty sufficient to secure that old wiring. Yours must have been a DD often driven during evening/night, seen that weaken wiring before where others driven less during dark hours are still fine today. 55w halogen = 5amps (4.5?) constant on that tinny wire
If I'm right i.e. the new ballasts let pass an incredible amount of init current (depending on the new circuit resistance) then that lil puff of smoke you've seen is no surprise. One way around that is to beef up the gauge size within the headlight assembly or ideally connect the ballast power rail to the battery directly. The latest being what many retrofiters does in fact and the safest set-up (requires extra wiring and some clever fiddling).
Are those new ballasts engineered for high power 55w or 35w? you know? In any case you'd want the small/cheap 35w preferably. No need to go overkill there...