My pool has never been that low on CH since I've owned it!
340 is easily managed. You've got nothing to worry about right now.
Plug all your numbers into poolmath. Don't forget water temperature. Look at CSI down near the bottom. Is it close to zero? Don't worry about it. If it's closer to positive .6, start playing with the numbers on the target side. You can't skimp on FC or CYA or salt, you have no control over CH or temperature, which leaves you with manipulating pH and TA. See what happens when you lower TA to, say, 70. You might find that turns it corrosive! See what happens when pH climbs to 7.8. Play around with it. You might just discover that lowering TA once and keeping a close eye on pH will see you through the summer. Maybe you won't be able to wait until pH rises to 7.8 before you add acid. Maybe you'll just have to keep it below 7.6 or something. Remember, CH will climb over the summer as you replace the evaporated water. The water will go away, the CH will stay behind. From my firsthand experience, when CH hits 800, it starts getting difficult to control things. You're a long, long way from that point.
If it rains during the summer where you live, grab as much of that free, zero-CH water as you can!