Running significantly higher than the manufacturer's spec won't give you the fuel economy boost you're hoping for - the gains are minimal and come with real tradeoffs. Yeah, lower rolling resistance means better mpg in theory, but we're talking maybe 1-2% improvement at best, which is basically noise when you factor in driving habits and road conditions. The 32 PSI recommendation exists because it balances fuel economy, tire wear, handling, and ride quality. Push past it and you'll get harsher suspension feel, worse traction in wet weather, and accelerated wear in the center of the tire. The sidewall 44 PSI is a maximum safety rating, not a target.
Here's what actually works if you want real gains: check your pressure when the tires are cold (before driving or a few hours after), because heat inflates them. A lot of people measure after highway driving and accidentally run high all the time. Also, a slightly underinflated tire (by just a couple PSI) versus one that's overinflated will wear worse and kill your economy faster than the small difference in rolling resistance. So staying within that 32 PSI sweet spot but keeping it consistent matters way more than chasing some higher number.
If fuel economy is your real goal, focus on the stuff that acutaly moves the needle - keep weight down, avoid idling, check your air filter, and ease off hard acceleration. Tire pressure optimization is real but minor compared to those factors.