If you're thinking of taking up Gardyloo's suggestion of positioning to DUB (or elsewhere) to commence the RTW
Then I'd suggest you drop MEL-CBR-MEL, and perhaps even MEL-AKL-MEL
and thus gain four segments which you can use at your leisure for say two return trips from BOS to elsewhere in Nth America

MEL-CBR-MEL can be purchased cheaply
and usually MEL-AKL-MEL is also pretty cheap
Check it on itasoftware.com

This itinerary, DUB-xLHR-GVA-DOH-DXB-MEL-LAX-BOS-DUB uses only 8 of the allowed 16 segments
So you could then have 5 flight segments in Nth America (you are allowed up to six, but you are already using one for LAX-BOS)
and still have 3 segments left over (so perhaps add MEL-AKL-MEL back in)

Getting a bit more complicated - fly into SYD instead of MEL, because it has better international connections. If you need to get to MEL then your add-on tickets could be SYD-AKL-MEL-CBR-SYD
Then fly back to BOS via Tokyo (SYD-NRT-BOS)
This will now allow you six Nth American segments to use at your leisure
And you'd still have 2 segments left - so perhaps use them at the end for a European holiday finishing up in DUB
And get back to BOS using some the frequent flyer miles you will have accrued on this trip
(you have thought about them, right?)

Lots of possibilities to explore