I have a new job where I will be traveling BOS-SIN 6 to 8 times per year, but it will only pay for premium economy. I'm AA gold right now and am on track to be platinum by August, which confers OW sapphire status. I may reach emerald next year.

Is there any greater chance of a complimentary upgrade from premium economy to business class by choosing a specific OW carrier for these flights? I could take JL, CX, BA or QR.

I've gotten op-ups on BA and CX from PE to business.
Both times I was emerald. You'll probably be the only emerald in PE... But at the same time BA is the worst of those 4 airlines in terms of PE product. Since you're accruing with AA at least you can upgrade ba with AA miles? Check the AA forum.
Also, these tickets will probably be expensive so flying ba would benefit you more if accruing with AA.

This may not be doable from a business/financial standpoint, but I thought I'd mention that a DONE3 business class RTW ticket with travel beginning in Norway currently carries a base price of $5225 which compares favorably to a number of PE fares bought on fairly short notice (which your frequency of trips might imply.) The rules for the Oneworld Explorer require a minimum of 2 stopovers (24h+) enroute, which would be easy if you started and ended the RTW in Oslo - one stopover in Singapore, the other back in Boston. The actual route could be something like OSL-HEL-SIN-NRT-BOS-LHR-OSL or OSL-LHR-BOS-HKG-SIN-HEL-OSL.

Depending on your personal or work needs/requirements, you could also use the ticket for a fair amount of additional travel at no increase in fare. For example, if during your time in Boston you want to use the ticket for travel to, say, California, or pretty much anywhere in North America (which includes Central America and the Caribbean) you could do so. Much depends on your or your employer's desires and policies. Maybe worth considering, anyway.

There are numerous threads on this board describing the Oneworld Explorer and its rules/benefits.

You have numerepous options for USA east coast to SIN. Many more options from NYC, including with SQ JFK EWR
https://en.wikipedia.org/wiki/Changi_Airport
A map from the Great Circle Mapper - Great Circle Mapper

With non USA airlines always expect to fly in the seat you pay for. Non USA airlines do not have the upgrade mentality. Even when pay for the upgrade with ff miles/cash co-payment.

Also note that QR, while almost certainly the best J product between BOS and SIN of those options, doesn't have premium economy.

True although the OP may be referring to comfort plus seats on the planes leased from CX.

Possibly, but I also don't think those frames routinely fly to either SIN or BOS.

OP could credit the SQ flights to AS and keep oneworld status.