I would delay until Sept., then stay in Baja or the highlands of Mexico for a while, as heaviest rain comes in late September. No rain in Baja and highlands have less rain. But depending on the year ... even October can have HEAVY rain. Varies a lot.

May/June is beginning of rainy season ... sometimes you can have NO RAIN until July. Also varies. But May and June are HOT ... really HOT and humid ... and many Brits get straight back on the plane and fly home once they
suss the reality of what real heat and humidity are. Horrible.

By October, things cool off and heavy rain subsides. (varies) Baja is a good place to kill time ... hot in Sept. but its a dry heat, more tolerable for most.

You could also spend time in California Sierra until mid to late Sept. then head South. Nice weather, good camping, many good roads both ON and OFF road.

In DRY season the Caribbean side of Nica, C.R. and Honduras can be a real adventure, great snorkeling, remote and not too touristy.

I don't know S. America roads well enough to advise. Meet riders/travelers on the road, get ideas, build routes as you go. Colombia fabulous riding, Ecuador too. Peru' well documented inland routes.

Keep reading ride reports, gather data. Take your time, plan rest days between marathon riding days. Take it all in ... and enjoy.