Ok, I managed to grab some time today and repair this thing.
Actually it wasn't Z41. That did have a signal after all, although it was hard to see with the scope.
No, Audronic was onto it. On some more reading I got very suspicious of Z5 (a 74C00) as it feeds the base of a transistor (Q2) in the video circuit. This transistor wasn't switching on because the voltage coming from this chip to the base was too high. When I checked the voltages on Z5, input was ok but output on one of the gates was screwy. Replacement with a spare 74C00 fixed that problem and lo and behold, video appeared!
So in summary there were two issues with this board, a power regulator IC and a 74C00 Quad 2-Input NAND Gate on video sync circuit. The arrows show the offending pieces of silicon.
Reassembled and running, it looks like this...
Yes, it definitely is Level 1 BASIC. Given L1 machines are not common (most were upgraded) I'm pleased to have it. It also came with a genuine TRS-80 screen although not the one shown here. The one this Level 1 unit came with is, ironically, more modern (and modern looking) than the one pictured. The former's in good condition though and works, so I'll use that screen with my Level II machine and this one (which is the original design) with my Level 1 unit.