Hey Bernie! My 502 was long gone prior to the arrival of the Thunderchild. IMO, the wattage output, the size and weight, the voicing (super deep, polite low and upper mids, bumped mid mids.. that head has a voicing a bit like a 'W') would not be the optimum for the little 4ohm Thunder Child. I'm sure it would sound find, but the smoothness of the ThunderChild in the upper mids, and the small 4ohm box and nice round low end favor (again IMO) a brighter, tighter, 400-500 watt micro head.
Given my experience with the LMII and F1/F500, any of those heads, the Shuttle 6, the GKMB500/Fusion, the SWR HeadLite, etc. would sound great and drive the cab to 'full volume'.
Edit: And... my appreciation of this cab and its unique design and performance grows by the day. Absolutely fantastic single cab solution for many gigs and contexts. Superb design and performance IMO.... by FAR the best small cab I've ever experienced (based on size, weight, low end performance, voicing, quality construction, max SPL, and the ability to generate true low end at surprising volumes with no compression or quashing).
I've made my first real change in gigging rigs in quite a few years. My current gigging set-up for the two locations in which I gig (I have two full sets of gigging rigs so I never have to fly with instruments or amps):
1) Road rigs: Bergantino AE410/Markbass F500 (Large gigs), Thunderchild/F500 (smaller gigs/tough load ins).... Alleva-Coppolo LM5.
2) Home/driving rigs: Bergantino AE212/F500 (Large gigs), Thunderchild/F500 (smaller gigs, tough load ins).... Sadowsky NYC Ash/Maple Vintage with singles.
So, after about a decade, no more Epifani UL, and after 3 years or so, the nice little Schroeder 115L+ is also gone (to my buddy Wilbyman, who is digging it for his tone goals!). I don't change often (although enjoy trying stuff), so this is quite a move for me!