Moose, you are overthinking the problem

Recommendation.

What railroad are you modeling?  What era?  In the 70s ti oresebt  the double track centerline was normally 16 to 20 feet apart.  In the 20s to 50s the track centerline was 13 feet.

For a high speed passenger line give yourself two passenger lengths to transition from the wye to the mainline track so you don't induce any "ess curves" into your track and by eye lay your track.  That way your passenger trains will smoothly transit the track with no violent moves or jerks and your engineer doesn't have to worry about the ladies in the parlor car spilling their drinks.

Eyeball it

A 3.5 wye is the equivalent of a #7 switch.

Just install flex track and eyeball in the flextrack.  If it looks like a smooth curve it will operate smooth.

Just install flex track and eyeball in the flextrack

Yeah ,much faster than trying to calc  it out. If you have the switch temporarily tack it and some flextrack down in the desired configuration and push some of your longest cars thru it to see how it works then adjust the design if necessary. Way more fun to play with the trains than to play with the numbers.

Over thinking a problem? Who? Me?

...You know me better than you thought!

Seriously, eyeing relative track placement would be difficult given what I'm trying to lay out. Working through the numbers makes it easier for me to understand what difficulties I might have and how to avoid them.

People enjoy RR modeling for various reasons, part of my enjoyment comes from playing with the numbers.

Oh, I should have mentioned, the reverse loop will be hidden, so I'm not concerned about the prototypical esthetic.

I found an Atlas no. 7 left-hand turnout that I am going to use instead of a 3.5 wye, and I'm going to assume a radius, based on NMRA standards. Here's the numbers, 'cause, ya'know, I like numbers...

Get out your Transit and have a ball

If the visual impact is not important, then you decide what you want L to be and solve for the solution.  If the visuals are of concern than L should be the length of the longest cars you plan on running.  If you want to be prototype than the frog numbers for the turnout should be a #14 or higher for a high speed situation.