It's been some time since I worked on these, though I now have 2 sick ones in the queue. I reckon T633 is the "easiest" of the 3 transformers to match, as T623 has to be tailored to regulate by variable DC saturation and T701 has to run all the CRT HV.
The drawing you posted indicates 3.8 to 4.2 mH for the primary, which is 100 turns, so about 400 nH /(turn)^2. Maybe start with that and your overall dimensions; I didn't do an exhaustive search but this
gapped N48 pot core looks sort of in the ballpark? Unlike the other two transformers I don't think this one is very critical for, e.g., magnetic losses etc.
As I recall both my previous 221's had other issues due to battery leakage, and I ended up fitting a miniature 2 watt 120VAC - 12VDC switching power supply, plus a one-transistor current source to charge the battery. This eliminated T623, T633 and all associated circuitry, and easily fit in the well between the batteries under the CRT neck. I believe I also fited NiMH batteries in place of the original NiCd packs.
Edit: here's the
thread on TekScopes from 2012, and the
schematic.