Looking forward to seeing more pictures, here are same the pair of boards fitted to my 5243L, not much difference in the rectifier board, but regulator board has some older looking Zeners and I agree the original capacitors are long past their best, the 100uF had been replaced in the 70's & was fine (had to desolder to check).
Counter is s/n 408-00459 made in England, so way older than the service manual with series 628-xxxxx. No level control on the front, only sensitivity switch.
Inside not much dirt but some signs of corrosion, especially transistor caps on board A19, A20, A21, A35 in the bottom are dull. Boards A10..A14 are the same as A15, A16, so populated all medium frequency decimal counters where low frequency decimal counters would be required only. Board A10 is populated with different transistors, so maybe replaced once.
Measured the caps on board A7 as well as C4, C6..C10 to be fine with about nominal capacitance and low ESR, so fired the counter up and had at least some signs of life (will recap later).
First digit does not come up (bad nixie AND bad board A10, detected by swappings around), not counting right. Oscillator is working and oven heating. So have to invest some time for a more sophisticated analysis. A separate thread, I guess.