On my way to PEN I did UA up to LAX, then LAX-SIN on SQ then had a 4 hour layover and flew Malaysian to PEN (interlined luggage). I did the Malaysian flight as the layover on SQ would have been too long.
On the way back SQ flies PEN-SIN and SIN-LAX without a huge layover in SIN so it was SQ all the way back to the US.
I'd recommend this type of routing unless you're willing to add an overnight in Singapore in each direction - in which case you could take UA to SIN then take the first flight out in the morning to PEN. Then fly from PEN to SIN some evening, then the next AM board UA back to the US.
Since you're a 1P, flying UA gives you double-miles, you lose ~17,000 RDM miles by flying SQ. Something to think about.