Give a couple of engine builders a ring and find out what they'd charge!
Couple of ideas to consider.
This will be the more expensive option but:
Have a chat to Paul Finch - see what he would charge for a forged rebuild on your engine reusing your crank if serviceable or even going for a 2.1.
Cheaper option could be to:
Give Andy Williams a ring or email (Williams motorsport) for a rebuild on your engine. My last rebuild was around £1.6k which was new bearings, gudgeon pins, Head Gaskets (Cosworth) and RCM Baffle plate. He's currently got
this engine on eBay which I appreciate is higher than your original budget (based on the options you were considering) however I'm sure he will take your engine in Part Exchange and bolt your heads to the block. My original build was done on a part ex basis and he sent back the engine with all my ancillaries re-fitted.
Either way a strong build on your engine could well end up being a cost effective solution as while it may cost slightly more in the first instance you wouldn't end up with the ECU itch that non-functional AVCS would leave you!
When you do consider taking the engine out I've got an engine stand here if you want to borrow one?
If the engine is being rebuilt or replaced, I'd certainly echo Dave's comments that an uprated Oil pump would make sense - I also echo his comments that many builders won't do a simple HG replacement for fear of imminent failure afterwards, however I know that my builder (Andy Williams) does not fully subscribe to that school of thought in fact when my engine has the same symptoms as Steve's (Ok mine was a forged 2.5) he spilt the book halves (no cost) to check the bearings to prove that there was no reason to replace them by default if it was a minor HG issue (Gasses to oil with no water contamination of oil) - his findings from my engine was that the bearings were in perfect condition with only minimal signs of wear in one with milage.