Can Double Mainsheet act as a traveller?

[toolarts]

I am the owner of a Rhodes Traveller 32, with it's typical double mainsheet rig.

It has two blocks at the end of the boom and attaches behind the corners of the cockpit coamings.

The double mainsheet is really convenient for tight maneuvering in the harbor. I can use either mainsheet just like a single mainsheet. For reaching and on passages, it is great.

However, no matter what I do, the mainsheets always pull the boom toward the centerline of the boat. There doesn't seem to be any way to harden it down on one side when sailing closer to the wind.

The only places to mount a traveller would be right in front of the companionway on the bridge deck (ugh!!); or on top of the cabin. Since this is a double ender with stern mounted rudder, the tiller sweeps the rest of the cockpit so the bridge deck is about as far back as a traveller could be mounted.

Do I have to install a traveller to get what I want?

Any ideas?