Sure I'll take this on.
Just buy an original TDi instead.
It's almost impossible to give an estimate for this kind of work. There's so many variables and unknowns when you're doing a motor swap (properly) that you have to have a relatively open budget, otherwise your car will never run properly. For example if the motor you're swapping in has 80 000KM, it would be wise to have the timing belt, waterpump, done, just to avoid having to do it 20K later. In that case, your swap just cost roughly 400$ MORE than the initial estimate. That's just one example, cause while re-installing everything, it's ALWAYS recommended to replace anything that is in average condition, so you may be looking at new drive axles, radiator, bushings, tie-rods, brakes, glow plugs, injection pump, glow plug harness, control arms, etc. Once the motor is up and running, it could flip codes for various sensors, driving up the costs again.
To be innacurate, an MK4 TDI swap into an MK3 needs wiring harness work, and custom intercooler and exhaust piping to adapt the manifold. Just wiring harness you're looking at about 5-10 hours roughly, plus if you get it done (and you should) by a top quality fabricator in stainless steel, you're looking at at least 700-800$ of custom piping if you go with a FMIC. Plus the labour to install the motor, and labour for testing (we always daily drive our swaps 3-5 days after the swap to insure that everything is tip top shape before handing the keys to the client). All that is essential to giving a properly running car back to the client and of course all that attention to detail is charged back to the client.
There are definetaly shops that will charge you a fixed rate, but beware of cut corners, you will likely have neverending issues with the car afterwards, and nobody else will be able to work on it cause they won't understand WTF is going under the hood because nothing is where it should be...