hmm sooo you are getting some interesting info, or relaying it poorly.
1) properly machining the head and block for a MHG is a big job, not because of the head but because of the block. to do it properly, the block should be removed from the car, disassembled, cleaned, and tested for cracks (same with the head, technically, but the head is easier to get off the car and disassemble/reassemble than the block). then the machinist can mill the deck of the block and get it properly smooth and flat for a MHG (i would shoot for an RA of 25 or less (RA = roughness average, and if the machine shop operator looks at you like "wtf is an RA" when you ask for it, you need to find another machine shop)). the block should then be cleaned again because bits and pieces of metal will inevitably get into places that will later cause engine failure if they are not properly cleaned out. this is why you cant machine the block deck with it fully assembled (or still in the car). if someone offers to lap your block while it is still in the car, chances are they are not gonna do a very good job and you will end up with a poor sealing surface for your MHG, which will ultimately lead you to another blown head gasket shortly after reassembly.
2) $800 would be cheap, in my opinion, for a proper job of resurfacing the head and the block. for a shitty job, i'm sure that is an ok deal.
i removed the head from my vehicle myself and took it to the machine shop. he checked my head for warping, confirmed hardness, did a full 3-angle valve job, and milled the mating surface to an RA of 12 for $450 bucks. He wanted another $350 for the valve adjustment, which is necessary after a valve job that changes the length of the valve train (like if you have your valve seats ground or your valve stems shortened/lengthened/replaced, etc). i noticed you mentioned the $800 was just for "machining the head and block". that sounds kinda scary. you should find out exactly what work they would be performing and how they would do it, i.e. will they disassemble and clean the head/block before machining, and then reassemble checking clearances and tolerances and using new seals/equipment where necessary.
3) typically, a 7m rebuild and a 2jz swap should not be in the same ballpark, cost-wise. whoever told you that was, in my opinion, full of shit. a 2jz front clip alone costs $2000. that is before all the labor to customize all kinds of shit in the mk3 chassis to fit the 2jz motor. and it doesn't include various additional parts you will need to make the swap happen.
a good 7m head gasket job, where the owner outsources ALL the labor and part purchases, should cost $3000 or less. and $3000 is a high figure. I called a local mechanic with a good reputation and requested a quote to repair my blown head gasket, and he said he could do it for about $1800 (this was a rebuild to toyota OEM specs, and included R&R for the valve train).
4) you should consider going with a toyota OEM gasket. sounds like you are trying to field a viable daily driver. MHG and the cost associated with it is more for people who want to build up their motors with lots of aftermarket parts and aim for high horsepower goals. these type of cars are not typically used in a daily driver function. with an OEM gasket, you only need to machine the head's mating surface, so long as the block deck is straight and isnt horribly scarred/pitted.