Before you give up and junk the vehicle, mainly because a 97 Honda is not worth the money to have someone replace the engine, there are simple tests that can pin point problems.
A shop can use an analizer, with a scope and gas tester, and perform a cylinder kill test. This will provide information on each cylinder, how they are firing, the firing time, the amount of unburnt fuel(and other gases) exiting the tail pipe before and during the test, and a relative compression test. This will pin point which cyclinder is missing, how it is firing(or not), and if the problem is possibly tune- up related or in the head or cylinders. Also;
1)- wet and dry compression test. This is a simple test to determine the compression in the cylinder, or lack of, and can be compared with the others. A wet test helps determone of a leak is a ring by-pass problem or valve seal, a blown cylinder head gasket, or bad valves.
3)- Radiator pressure test. This is usually performed with the plugs out and either a good ear or a tester. If the system can not hold pressure there is a leak. If there is a small leak outside the engine it can usually be found. A good ear or tester can tell which cylinder the leak is in if there is one.
NOW: before you go off the deep there is more. A white spark plug does not mean there is an antifreeze leak. A mark on the rotor(roater) has nothing to do with the antifreeze. A miss and a wet plug, along with an antifreeze smell(very strong and easy to detect)), would be indicative of an antifreeze leak. In fact a plug burning with a white color is a good thing. What would they want, black, green or orange? A search on the internet can get you pictures.
I am not saying you do not have a head gasket leak. You did not mention the vehicle losing coolant, or running hot. These are signs of "a leak" to be determined and one or more of the above test to verify.
It sounds to me like your engine doctor is a quack.
Do you have reason to believe the original shop ripped you off? Maybe you need to consult with them and see if a new part went bad, a part was not replaced properly, or another problem occured, such as a major vacuum leak.
Explain that for $560.00(you did not explain what they did) you feel they should look at it. If they are into customer satisfaction at all, or a reputable name, they will be happy to check it out.
Use the sob story of being broke---needing a vehicle-- and having spent a lot of money to still have a problem.
It would be interesting to know when the "miss" occured? Shortly after the repairs, a long time, and how many miles?
You really do not need to spend money on a probability. I feel you(and others on here) will agree.
"I think it could be", or "it might be", or "it is possible", are all words meaning one of two things.
1)- You need more testing to determine EXACTLY what the problem is or,
2)- You have just had an idiot look at your vehicle and stay away from there and warn others.
This blows my mind. "You have a miss, "might" have an antifreeze leak in the engine, so you need a new engine". Wow!!
Do you lose coolant? Does it run hot?
If you did possibly(one of those key words)have a small antifreeze leak(inside the engine), with the evidence being a loss of coolant and thus running hot, in such an older car that is not classic matierial, or a family heirloom, I would simply buy a can of engine stop leak and follow the instructions to the letter.
I would stick with the fact that you saw a quack(nursery rhyme) and get a better opionion.
If I know all this as an "ex" technician that has been driving a truck 15 years surely someone where you live is smarter than me. By the way, I was REALLY really good at what I did.