While not specifically designed as a bluewater boat, the Geminis have made several circumnavigations as well as trans-oceanic passages. The blog of one that is currently making a circumnavigation is that of Slapdash
Larger boats, to a point, are going to be more seaworthy. However, given the budget constraints you have listed, getting a larger catamaran in decent shape is pretty unlikely. Also, I'd point out that the larger the boat—the more expensive the maintenance, mooring, dock, slip, and haulout fees are as a rule. A Gemini is designed so that it can be kept in a single width berth in many marinas...
I'd also point out that the scantling rules for multihulls is a bit different than that for monohulls. Monohulls have to be built much heavier to withstand the pounding seas due to having to carry all that weight around with them. Multihulls get beaten up a bit less since they tend to float on top of the waves rather than having to bash through them. That said, yes the Geminis are built a bit more lightly and to a specific price point than other catamarans, but it does give you a lot of boat for the money.
There are several Gemini owners on this forum that probably will be along to comment specifically about them.
In terms of full disclosure, I would point out that my boat, a Telstar 28, is made by the same company as the Gemini 105mc and I've sailed on Geminis and have several friends who have owned different versions of the boat over the years. Some of the issues I have with my boat are probably similar to those that Gemini owners have, but overall, I love my boat and wouldn't hesitate to get another one. My Telstar 28 is also probably the most heavily modified from stock of all the ones out there currently.
They're not perfect boats, but they are a decent boat and a good value IMHO.