I'm surprised you can't find a 200 or 300 Tdi. I admit there aren't as many, these days, but still. A 200 is by far the easiest and cheapest swap, literally just bolt it in.
Yes a Td5 can be swapped in, you can either try and make it like a factory install, or you can just get it in and adapt bits. The latter will likely be cheaper.
You'll need new engine mounts welding in place and depending on which gearbox/bellhousing you may need to look at moving this too. Although ideally you will want to retain stock propshafts unless you want to splash out on custom ones.
The Disco box uses a different top linkage, not sure how easy/cheap it is to convert to a Defender one, I think it's possible, but never done it myself. If you don't do this, the gear stick will end up in a different place, closer to the middle seat/cubby box area. Which is fine, but will need some fab work and customisation to the seat box.
Note some D2's also don't have a centre diff lock (they rely on the TCS). Some have it, but not the linkage. So you may want to investigate what you want to do here.
I think the D2 uses a long bellhousing like D1's did too, but I don't know this for certain.
You'll need new exhaust, or at least front sections, intercooler and rad. Stock Td5 Defender items will all fit. Overall the Td5 swap is fairly easy, but expect it to cost you a fair whack. And make sure you get all the wiring and ECU. You may also need a Td5 speedo. And I'd advise getting a Hawkeye or similar diagnostic tool.
The Td5 is a lovely motor and responds well to tuning. A friend converted his 300 Tdi 90 to Td5 and it goes very very well. But cost a small fortune. Although he was going for a complete factory look install.
If you are looking at other swaps, then I'd also consider the Rover V8, it'll be more juicy, but they are lovely engines still. The BMW 2.8 petrol engine can also be used (was fitted to South African 90's) and the M57 3.0 BMW diesel from the L322 Range Rover.