There is plenty of opportunity for DIII players. It's probably fair to assume that all DIII players aren't interested in giving up their summers to baseball, but there are plenty of passionate, commited guys who are....and the opportunities are certainly there. You might not have a shot at the Cape, but my son, a DIII pitcher, played in the Coastal Plains league....successfully. Did well, got lots of innings, selected as an All-Star.....and he wasn't the only DIII player on his team. They went and grabbed one of his teammates mid-season when they needed a replacement. Across the CPL, there are DIII players on many teams. (But not many......)
Coaches have connections, sometimes openings come up towards the end of the season, as other players who were signed to summer teams in the fall, get hurt, need to go to summer school, etc. Son's college team placed 4 guys on CPL league teams and a couple others in another NC league....so there are places for the committed to play.
Ask the coaches at the schools you are considering what there views are on summer league participation....and where their connections are.
Good luck.