He'd absolutely overthink it to hell and back.
We're talking making notes and charts and a list of Everything That Must Go Right for the Perfect Setup. He's made a list of seventy-three options and eliminated half of them. He's fussed over the ring and has three different options stored in his sock drawer, one in the bottle of shower gel Bill doesn't use, and one up in the rafters. There's an excel file with probabilities for weather and temperature and the mood Bill might be in at that exact moment.
Of course, all these things completely fall apart in the most chaotic manner possible, with a high chance of 'near-death experience' to boot.
Dipper ends up blurting out 'Marry me' after the battle, seizing Bill's hand while his own are all sticky with the blood of their enemies and the survivors groan in anguish in the obliterated wreckage. And it's the most romantic proposal Bill could ever ask for.