My opnion:
You could, I just looked up the specs for the two boats, the mast is in the same location same height, the only addition is the bow sprit, hardware and the forestay brought down to the stemhead.
However I would recommend leaving it as a sloop and installing a solent stay, (Provided that the boat is well balanced now) this will be cheaper, easier, and more functional for cruising than the cutter rig is going to be, especially short handed.
If you have to have the cutter because of the aesthetics, you can convert it to one by adding a bow sprit, while rerigging the boat. Since the rigging needs to be replaced on your boat anyway, it could be done at the same time. However it would add some
significant cost to the project. Depending on your skill level the project may be within your abilities to do it yourself and save some money. Custom hardware for the bow sprit are likely to be your highest cost in adding it. A Gammon Iron, Bitts which include a mounting for the bow sprit, the bobstay fitting, and cranse iron will likely add up. When you add in the cost of a new pullpit, and a new roller furling unit, a staysail stay bracket, Running back tangs, running backstay pad eyes, running backstay tackle, stay sail track, stay sail track backing plates, New Life Lines, and all the other stuff that would be part of the project it is going to be an expensive, and time consuming project. Unless you are accustom to boat projects and the time and money expansion of such projects, I would not recommend it as a project.
Normally I would recommend tackling the rest of your project list first, getting some sailing time in on the bay, and then making rigging decisions like this. However having seen the boat myself, I would suggest that the prudent course is to evaluate this issue and replace the rigging as soon as possible. My recommendation would be to rerig the boat as is with the addition of a solent stay over the traditional forestay; you can have a heavy weather sail plan without the added expense and annoyance of running back stays. The 40 sq feet difference between the sloop and the cutter (8% or less of sail area) could easily be made up by bringing the jib a little closer to deck. New high quality sails would be higher on my list than 8% of sail area.
PM me your phone number and I would be happy to talk about your boat with you for a few minutes if you would like. I looked at that boat for a friend a while back and have the photos, although I can't find the notes that I took at the time.
Guy