Installing a cockpit enclosure is impossible
With all due respect, I would suggest different wording. I have seen this done on a lot of boats with bridgedeck travelers and they have a full dodger with a bimini, with a gap in between. At anchor or at the dock a zip-in fill piece closes that gap; if there is a lot of rain, some owners have a snap shackle on the main tackle, and move the boom out to a position over one side or the other to keep most drips out.
So, having a full enclosure makes dodger design integrated with a bimini more challenging due to the extra panel.
Having seen it done many boats, my take on this is that an experienced canvas shop can do this easily. Adding the side curtains to achieve full enclosure is about the same, either way.
Since all the bimini tops I have seen do have a zipper connection with the rear of the dodger, this section uses a zip-both-ways piece (s) to fill the center when desired. A dodger & bimini structure was built like this for our boat, years ago.
BTW, I sail with a buddy with a 35 footer with "full canvas" -- and removing enough covers and side windows, including the cover over the vision window in the Bimini top, is time consuming. This can reduce time spent sailing rather than motoring.

(No problem when you have several enthusiastic sailing friends aboard to assist you, but lot of covers and vision-reducing windows may reduce sailing time when it's just you and a spouse/family that are already ambivalent about sailing. )
Addendum: Make damned sure that your boats cabin top will take the considerable forces of the new traveler. Budget for ball-bearing blocks, including the mast base turning block. Also a new ST winch on the rear of the housetop. This change in sheeting will make single handing a good deal more challenging, as well.
A quick look at basic data shows your mainsail area at approx. 230 SF, compared to 250 SF for our boat, That's a
lot of sail, and the load on the main sheet would really jump up if that sheet were attached more than halfway forward on the boom, as it would appear to need to clear your hatch opening. Some deck/house load and rigging engineering would be required, best done by a NA.
Lots to consider, and considerable money will be required. Spending $5K (or more) for the full package of canvas, windows, and covers kind of gets one's attention. If you are OK with the compromises, and plan to enjoy your boat for at least another decade, it will all amortise out OK, strictly IMHO.
Good Luck whatever your decision!
