I don't think you need to be too worried, but you will probably have to do a few detours.
Map 5 should be no problem - it won't be that hot, nor too cold at Big Bear.
Map 4 will present the first challenges - esp. with the Western Divide Highway.
The main roads in Sequoia NP and Kings Canyon NP should be open.
If you have the time - and you may wish to stretch it a bit early on -
You really should head on up into Kings Canyon - worth it.https://www.nps.gov/seki/planyourvisit/road-conditions.htm
Yosemite Valley will be stunning this May. Have you ever been there?
The first time is always so amazing for everybody. Esp. in May.
So, do not, under any circumstances, skip Yosemite - even if you have to detour.
You will be coming in from the South Entrance and have your first vista past the tunnel.
Although not posted, people cycling into the park can camp 1 night at the backcountry campground.
(This is NOT Camp 4 - way better - on a bend of the Merced River - but you have to ask at backcountry office.)https://www.nps.gov/yose/planyourvisit/tioga.htm
More than likely, Tioga Pass will still be closed - they May (5% chance) let cyclists thru.
Most likely you will need to detour via Sonora (Hwy 108) or Ebbetts Pass (Hwy 4) - both have very steep grades.
There is a big climb out of the valley to Crane Flats - Hwy 120 is not my favorite, either.
If you have the time Hwy 140 to Mariposa is lovely along the Merced River and way less traffic.
The east side of the Sierras should be no problem. Monitor Pass usually opens in late April.
Traffic should still be pretty light north of Topaz - but campgrounds may still be closed.
Lake Tahoe will be stunning will snow-capped mountains and blue water - - but chilly.
Map 3 has a couple of challenges and question marks.
First, I don't know why ACA routes you via Graeagle, Quincy, Greenville on Hwy 70 - which is kinda sucky.
There are great 95% paved county & forest roads via Loyalton & Chilcoot then north -
Or via Calalpine and Beckwourth then north - coming out via genessee and Taylorsville.
Perfect time of year, too.http://www.papermapsonline.com/home/NorthernCalifornia/PlumasNationalForest.aspx
(Poor server, but give it a few tries and it will come up - esp. with new tab)
You can pick up a Plumas National Forest Map in Truckee.
The next challenge is Lassen Volcano N.P. - the main prak road may not open until June.
Your choices are to skip the park and head north to Hwy 44 via Westwood and Hwy A21 -
Or to head into the park as far as you can go, then return to the dirt forest road from Mineral to Viola.
Next is a choice - I think that it is highly immoral, although legal, to bike on interstate highways.
The ACA route takes you around Mount Shasta - lovely - but you have to do some interstate, too.
Another option is to head north from Old Station via Bieber, Lookout, and Lava Beds N.M. to Klamath Falls.
I am almost certain that the loop road at Crater Lake will still be closed in early June.
If so, then you can still ride into the park from the south but will have to use Hwy 62 & Hwy 230 to go north.
Whether you ride via Mount Shasta or Lava Beds, you should consider riding via Rocky Point on Upper Klamath Lake.
So we've gotten to Map 2 and it should be warmer - in fact, Crater Lake might be you last detour.
If possible, do the Windigo Alternate - US 97 has wide shoulders, but insane traffic.
Bend and Sisters are super yuppie - but have all services - esp, bicycle needs.
US 20 over Santiam Pass also has a good deal of traffic -
You can take the longer McKenzie Pass option - if open - Hwy 242 then Hwy 126.
From Detroit to Hood River should have few cold weather issues.
In southern Washington, do consider taking the side trip to Mt. St. Helens N.M. - worth it.
Also, there is a lovely, paved forest road from Packwood to Longmire in Mount Rainier N.P.
And you can camp just outside the park - they have no hiker/biker sites in the park - boo!
Then Map 1
It's a pretty brutal series of climbs over ridges in the park to Hwy 123.
And I don't know why the ACA routes you over White Pass on US 12 rather than Chinook Pass on Hwy 410.
Tipsoo Lake, at Chinook Pass, has one of the most spectacular views of Mount Rainier.
Then Hwy 410 is a sweet, quiet ride down to the Naches Valley and fresh cherries in June.
The Yakima Canyon along Hwy 821 is sweet - hike across the ped bridge at Umtanum Creek to camp.
North and east of Ellensburg (all services) there are two options.
The ACA route largely follows US 97 - pretty busy in Washington, too.
A lovely, but challenging option is to head east from Ellensburg on Old Vantage Highway.
The challenge is getting across the Columbia River - the I-90 bridge has no shoulders and fast traffic.
There are three ways to get across:
1. Pick a low traffic time - just before sunrise, light but no blinding sun, and ride like hell.
2. Ask or pay someone at the motel/store/campground to shuttle you across.
3. Hitch a boat ride to the Old Vantage Highway landing on the other side.
If you can do #3 it is super worth it. Esp. if you camp in Vantage, you have time to arrange #3.
The old road on the east side heads up Frenchman Coulee - stunning, sheer cliffs.
Then the south service road to George, Hwy 281 to Quincy, and Hwy 28 to Wenatchee.
Next up - when you get to Chelan, do consider taking the Lady of the Lake up to Stehekin.
You can take your bike with you and ride deep into the rugged country of the North Cascades.
By the time you hit the Methow Valley, it should be green and lovely - despite last year's fires.
And Hwy 20 over the North Cascades should be long open with all campgrounds open, too.
Just a few suggestions.
Have a great trip.
The Three Sisters - near Bend, Oregon