I bought my cruiser for 1600 and have 2500 into it now. I'm glad I'm keeping a spreadsheet. I know how things add up, and fast. 4k seems like a high number but if that 4k takes the engine to another 200k miles is it worth it? I'd think so but that is a really tough spot. My rig is a beater and I was seriously considering it. I'm glad I just gasket slapped it and replaced heater hoses.
I would try doing the hg replacement and see how long it lasts. The reality is it could last 10 minutes or 10 years. Worth the gamble? I think so.