The problem may not be the Western Express in April,
but rather, the TransAm in Colorado, Wyoming, & Montana in May.

It's been a very dry winter so far in the Sierra Nevadas - that could change -
but I do not expect the snow pack to be more than 66% this spring, probably less.
Snow and significant cold are still possible around Ely and Bryce Canyon, however.

But if you started in mid April, you would be turning north in early May.
Very few national forest and national park facilities open before Memorial Day.
Same goes for private facilities from campgrounds to cafes. Not all, but many.
There is almost always a significant high-altitude snow in May.
I know, I have lived in Wyoming for nearly 30 years and have X-C skied well into June.
If you were to hit Yellowstone around May 22, you will find very little open.
Heck, the South Entrance isn't scheduled to open until May 11 - Dunraven Pass, May 25.

<<<>>>

I have 30+ years of touring experience and 100,000 miles.
I have discovered that I can either pick a route and then try for the best timing on that route -
Or I can have a specific time period and then pick the best route for that time period.
But I cannot make both happen.

If you haven't toured in 5 years, but enjoy touring, why set yourself up for disappointment?
You can bike into Tahoe - or there are trains, planes, and buses.
A route as you suggest is best done starting in mid to late May.
I have done variations of that circle four times. And still had snow & cold.

https://www.cycleblaze.com/journals/wna2005/

If you want to stick with mid April arriving at Tahoe in early July -
I would stay further south - Route 66 for ex. - then head north west of the Rockies.
Spectacular country in western Colorado, eastern Utah, Yellowstone, east slope Montana.
Of course, you would need to create your own route.