Try it and see if you like it that way.... but you could save yourself a trip forward and having to reave the sheet every time, if you simply attached a 3' tail to your sail's clew and connect the sheets to the tail.
That's exactly what I did on my asymmetrical....
There are race versions of this set up... here are some examples taken from the
Annapolis Performance Sailing site:
Asymmetrical Spin Sheets - Bridle
Our bridle sheet system helps you get the chute around fast (key when jibing an asymmetrical spinnaker) by preventing the clew from getting stuck on the headstay. We make these up by stripping the cover from Dyneema cored double braids. The uncovered ends are spliced together, leaving one line to be attached to the clew. The single tail that is tied to the clew is generally around three feet long. Please specify your length requirements.
Asymmetrical Spin Sheets - Three Part
This is a great method for attaching sheets to an asymmetrical spinnaker. Here we make the sheets by stripping the cover from Dyneema cored double braids. The cover is left on in the areas that are cleated, winched and handled. The short piece is luggage-tagged directly to the eyes on the end of both sheets, then you can tie the ~3' tail directly to the clew of the spinnaker. This setup prevents the clew from catching during jibes
I use a similar, but less hi tech, setup for my asym.... note that I jibe the sail only, and the sheets are run around the headstay. Even though you prefer to furl and tack the sail through the triangle, this configuration would still work more efficiently rather than going forward and shifting the sheet to the other side.