Would I? Most certainly. But that's because, after over 40 years and over 100,000 miles of JR sailing, I couldn't possibly go back to the dark ages of sailing under bermudan rig.
Should you? That's harder to answer. Most folks considering a conversion would go for a boat from a previous era (like my Hunter Duette, really a twin keeled Sonata, in its day a sporty club racer/Minitonner, so with some of the same ethos as your Django). Their investment would be much less than for a Django 6.7, which is a relatively recent design (currently on sale for around 45,000 euros, I see). So less to lose on the resale value if, for any reason, the conversion turns out not to be a success. I guess it depends on how much of a risk-taker you are. I do think that you should put in more research and study than for a lesser-value project - not to learn whether you're really going to like junk rig, I'll take that as a given, but to find out which particular variety of junk rig is going to suit you and the boat best. Are you planning on club racing in Poole Harbour? If so, you should go and see the split junk rig on Amiina. Edward Hooper has it as his main aim to develop a form of the rig that can compete on equal terms against the pointy-tops, and puts in very creditable performances in the Round The Island Race. I'm nearer to the other end of the spectrum, having converted Weaverbird with the aim of spending all summer aboard, full time, roaming as far and as widely as I can within that time. Both boats and rigs perform very well; and both rigs are of a type which could be fitted to Zigzag, but are very different in concept. Where do you fit in the spectrum? Possibly somewhere in the middle, with a cruising ground ranging between Salcombe and Chichester, which might indicate a different form of the rig.
Could I? I think so, but I can't find enough drawings and photos to be sure where the mast is going to fit, and what the issues are going to be. I'd be looking for a tapered aluminium alloy pole for the mast. We have to go cap in hand to the street lighting and flagpole people to ask for a bare pole before they've cut into it, or mounted any fittings. Unfortunately, I hear that the source of my mast, Aluminium Lighting Company, don't want to oblige any more, but https://www.flagmakers.co.uk/bespoke-flagpoles/architectural-flagpoles/ may be a possible source. I'd want their 10m long, 165mm diameter model. For club racing, I'd choose carbon fibre tubes for the battens and yard, and I'd use Code Zero sailcloth for the sail. For my end use of cruising, I chose a heavy soft cloth, Clipper Canvas (seconds quality from Englishseadog), that is easier to live with.