@jea48
The replacement GFCI breaker is a good alternative, if somebody manufacturers a retrofit for what is likely a 60 year old breaker box. Ideally, OP would hire an electrician to install a dedicated 20 amp circuit and verify that the sub and main panels are properly grounded too.
I figured a replacement GFCI outlet was the simple "fix" he requested, however, his wiring does add another layer of complexity. The grounding issue could easy snowball into a large, expensive project.
Agreed, the best fix is to hire an electrician.
**406.4(D)(2) Non‑Grounding‑Type Receptacles.**
Where attachment to an equipment grounding conductor does not exist in the receptacle enclosure, the installation shall comply with (D)(2)(a), (b), or (c):
(b) A non‑grounding‑type receptacle(s) shall be permitted to be replaced with a GFCI‑type receptacle(s). These receptacles or their cover plates shall be marked “No Equipment Ground.” An equipment grounding conductor must not be connected from the GFCI‑type receptacle to any outlet supplied downstream.
(c) You may also install a grounding-type (3‑prong) receptacle without a ground, if it is protected by a GFCI (breaker or receptacle). In that case, the receptacle or cover plates must be labeled “GFCI Protected” and **“No Equipment Ground.”