I totally understand the worry, but honestly at one month in, 30-60ml per pump is not uncommon, and supply can take a few more weeks or even months to settle and increase, so you're not behind. Every body is different though, so it might be good to check with a lactation consultant or your PD just to rule out any latch or positioning issues that could be holding you back, because sometimes a small tweak makes a big difference.
On the 2-hourly pumping, more frequent pumping can help signal demand, but it's also about consistency rather than perfection, the missed 4-hour stretch at night won't derail things, and honestly burning yourself out won't help your supply either. I'd say stick with what you can sustain right now (your 3-hourly rhythm sounds solid) and give it another 2-3 weeks before making big changes like switching pumps or drastically upping frequency. A lot of mums I know found their supply climbed gradually between weeks 6-12 without overhauling everything, so don't lose hope yet.