How about Hawaii?
A quick review of the most recent edition of Latitude 38 will reveal that there were three Ericsons that recently raced from San Francisco to Hawaii (one 30, and two 35s) -- all single-handed. This race is held every other year and sponsored by West Marine. Not only did the Ericsons do well, the 1971 Ericson 35 won its class and was the oldest boat in the race! IMHO, the later model E35 III are even tougher, better appointed, more stable and sea kindly. That's a long answer to a short question; yes, I think a 35 III should provide what you need for your offshore adventures, provided the boat is in good shape and the gear is all current (that applies to just about any boat!). BTW, reports from those who participated in the race say that the boats spent the first three says in nearly 30 knot winds and very serious seas; if a 33 year old Ericson can survive that to win, I'd think a later model would fair as well.