That surprises me , long time since I had in my hand a (paper) WTT for the Met
, the Piccadilly is a very pleasant ride - but seems very slow compared to the Met Main. !
All of the Uxbridge trains run through to/from the City, except for a handful of peak hour additionals that start at Baker St, at the times the OP is likely to be travelling there is one at 17.41 and one at 18.12, and then at 18.44.
The Uxbridge branch is by far the busiest of the branches of the Met line and it is common for customers to be standing all the way to Eastcote, although if you get on at Baker Street you’re more likely to find a seat than those boarding at Finchley Road.
I would second this as something you should seriously consider. Given that you're seeking this information already, I would say it's likely that your stress would indeed be exacerbated by daily peak Z1 deep tube journeys, however the alternative on-street option to the much more civilised Baker Street trains is a great alternative, and honestly wouldn't even take much longer (after discounting the time taken to reach the lower level platforms of the stations on Piccadilly, and wait for a few trains to pass).
Given the scarcity of trains starting at Baker St, I really can’t see the point. It’s not like you’re coming into a Mainline station and have to hassle to interchange to the other line or are having to pay a premium for LU travel, it really is quite easy and costs the same.
Any time spent on the Jubilee line will really be quite small; I’m guessing from the Google Maps screenshot above the distance from the origin to either Green Park, or Piccadilly Circus is fairly similar.
The journey time on the Piccadilly line is about 50% longer than the Met from Baker St, but once you account for interchange and the Jubilee line travel time it probably isn’t much more than 10 Min longer. Always get on the first train and change at Acton Town and or Rayners Lane, as the Piccadilly line often starts trains at Acton in the afternoon when there has been any sort of problems on the lines.