At 1 ft, 4 sec with light winds, I'd say fuel-range is your only limit as long as you have a good VHF, EPIRB, PFDs, and your engine is well-maintained. It's all about confidence in your equipment and ability at the helm at that point. I used to run to the Liberty Ship about 20 miles offshore out of Packery Channel during snapper season in a jet ski, which is essentially a 12 foot boat with a 0 degree deadrise. There was also a guy who ran a 13 foot whaler out there in the same conditions. Just get comfortable going offshore and build up your confidence. I worked my way up from 3-4 miles offshore to 25-30 miles offshore on the ski over two years.
As others note, the wave period and wind are just important as the height. For the wave period, I'd shoot for 3 times the wave height. 4 times seems a little conservative and you're really going to limit your days. 2 foot 6 seconds in 10 mph wind is nice. I wouldn't go out in anything over 2 feet unless it was really nicely spaced--like 3 feet 10 seconds or more and light winds. And even then, I'd stay in state waters. And keep a close eye on the weather, not just current conditions... Things can pick up quick as you can see in this video, where I put up the live buoy data at some points in the video so you can see how the ski reacts to different conditions. You get to see a nice 2 foot 7 seconds, then 3 foot 4 seconds, all within one hour.
And slow down. Even in 1 foot, I expect you will pound if you run at your normal cruising speed. No need to do 30+ mph or whatever speed maximizes your fuel economy if you're only going out 10 miles or so. Any time it's calm like that and the bay boat fleet comes offshore, it is a mad house out there with Channel 16 getting busy. I feel like they're always cruising around at 35 mph+, pounding and going airborne off every other wave, breaking things on their boats.