"The problem I found with the 4 speed on the 350 is that relatively large gap from 3rd the 4th" Amen Brother!
All too true, but one of the features that attracted me to these dinosaurs in the first place
was that Weird Alice 4-speed lathe-sourced/adapted gearbox. The point was to get the actual 1940's riding experience. That wide ratio 4 speed saves 4th for flat ground. Other than that, on any hill or into any headwind you go the speed
the machine allows you to, in whatever ratio serves the purpose of propelling you forward. It was all vastly better than walking in 1940. H's also has additional gearbox ratios, a "road" and a "trials" variant for not a lot of cash. Being a pre-unit design, gearbox ratio changes are possible of an evening with the engine
still in the frame. Coming from a Japanese bike background, that was a novel concept indeed.
The 5 speed really improves the rideability under modern "combat traffic" conditions. There's always a suitable ratio at hand, you are more able to tune your road speed to accommodate traffic. Paul W's souped-up 350 Bullet would
really shine in that environment. My stock ES350 requires a sharp eye on the rear view mirror and a mental map of the "good" turn outs, as there's no way I'm letting some yobbo tailgate me long enough to get him wound up for a "desperation/frustration suicide pass". Lucky for me I have a suitably rural area, lots of 25-40 MPH twisties, so Black Mollie is adequate for the job. My 500 Bullet has enough Ongawa to make the 4 speed adequate in normal traffic, but it's not comfortable, you are always strategizing. With the 4-speed you rather need to plan your shifts ahead of time, the 5 speed removes that concern. For 1940's roads & traffic, the 4-speed was great. Here in 2020, you really need to pay attention.
"The other disadvantage of the 4 speed is the less than certain gear selection" Again, complete agreement. But fettling that anachronistic clockwork shifting mechanism into functionality is another source of satisfaction in owning these machines, at least to me. I've poured over Snidal's manual, replaced the bellcrank indexing detent plungers, replaced & filed the shift stop "butterfly" plates and "tuned" the rotation angle of that weird ratchet plate assembly, all of it fun.
I approach Bullet ownership/stewardship more like an opportunity to participate in "Early Days" tech than any search for performance. I'd already put plenty of miles on my old "UJM" SR500 Yamaha and had lots of various modern 4 & 2 cylinder road burner time. My rural location more closely replicates the operating environment of the 1940's, so here, these Bullets are largely adequate as is. Paul W has a much more "combat driving" environment to contend with, and his 5-speed and engine power mods have brought his machine up to the task brilliantly. Pretty amazing for what's basically a Pre-WWII design.