Thanks for the responses! In particular, the suggestions to transfer to bus or taxi @ Tottenham Court are really appreciated. While I wasn't trying to eliminate 100% of the stairs, it seems like adding in buses is potentially even faster than transferring to another tube line. The pointer re: single step access to buses was also an eye-opener. This combo would eliminate the risk of escalator breakdowns at Embankment throwing a wrench into the works.
I did eventually find a video of someone walking through the station and it turns out that the walker follows the exact path of interest.
Video around 18:20 DEFINITELY shows walker standing on Northern's SB platform #4 - i.e. exactly where we'd end up if we decide to take Elizabeth Line from LHR and change to Northern at Tottenham Court, exiting at Embankment instead of Charing Cross. The walker exits the platform directly onto an escalator going up. At the top, walks straight off the escalator (with a slight jog to the left) and follows signage toward Northern NB platform 3/Bakerloo platform 5+6 (probably ignoring nearby "Way out" signage). When this walk dead ends (with District/Circle's WB platform 1 on the left and EB platform 2 and "Way out" sign pointing right), walker turns right, goes up 3 steps, and THEN follows "Way out" signs up escalator to exit gates and finally walks out to Villiers Street. So this video shows you can get off a SB train and get directly to street level via escalator with just 3 small steps up along the way.