DONE4 for review
 

My first RTW, an AONE5, is about 75% done, but I want to nest in a DONE4 ex IST starting next month.

This is the plan:

IST-LHR (5/23, break, and take LHR-TPA round trip flights)
LHR-SYD-WLG (~6/15, vacation time)
WLG-BNE-SYD-CGK (~6/23, business stop)
CGK-HKG-JFK (6/27, return to TPA on DL flight)
TPA-DFW-LAX-SJU-TPA (any July weekend mileage run)
TPA-DFW-YVR-LHR-HEL (8/9, business stop in HEL, get BA flight ex YVR)
HEL-LHR-IST (8/15, may or may not fly last sector)

The Validator says this is OK, and is 18 segments and 47,120 miles.

The only required stops are Wellington, Jakarta (not neccessarily in that order) and Helsinki (last).

Any suggestions for improvements, and/or for using the 2 additional segments?

You can't do LHR-TPA-LHR on this fare if you are coming back to the USA en route to IST. You also can't do it on this fare as you can't cross the Atlantic 3 times (it's only allowed once).

You could squeeze in another mileage run in Asia, for instance CGK-HKG-CMB-HKG-JFK. And you can get another 50 miles or so by doing WLG-MEL-SYD instead of going via BNE. Alternatively, you could get a separate ticket for the trans-tasman leg, and use the remaining SWP sectors for a mileage run in Australia.

The LHR-TPA-LHR roundtrip is on a separate ticket if I correctly understand the OP.

Yes, a seperate ticket.

I'll play with some Asia mileage runs to see if there is anything that appeals.