Mid-April to mid-May is still the middle of winter for most of the Oregon PCT. In an "average" snow year, you won't have relatively snow-free hiking until early to mid July for the higher sections (Crater Lake, Mt. Thielsen, Three Sisters, Mt. Hood).
I suggest the southwestern US, where there are several long trails. You could do the New Mexico section of the CDT, which will give you a start on your third Triple Crown trail. Depending on how much snowpack and when it melts, your time frame might still be a bit early for some of the higher elevation sections.
For future years, try to get July, August or September free for your hiking vacation for relatively snow-free travel.
Here's a plot of the current year, prior year and 30-year average precipitation and snow water depth for the Mt. Hood Snotel, elevation 5370 feet:
Please note that the depth is snow water equivalent--assume the actual snow is at least twice that depth. Note also that the average peak snow depth occurs about April 28 (in the middle of your time frame). The average snow depth will be about 120 inches (3 meters) and there will still be considerable avalanche danger in the steeper sections, generally lasting well into May. Areas such as the Three Sisters and Crater Lake are a couple thousand feet (600 meters) higher than the Mt. Hood Snotel.