Absolute twist rate requirements are not written in stone. Whether this is because a given twist barrel may not be exactly the stated twist rate, or (more likely) there is not a well-defined gyroscopic stability coefficient (Sg) necessary for a given length (weight) bullet is debatable. Nonetheless, Bryan Litz recommends a twist rate for a given bullet that gives an Sg of 1.5 or greater. This is probably fairly conservative. I've shot loads in F-TR where the predicted Sg using Berger's Twist Rate Calculator was in the neighborhood of 1.4. They worked just fine. According to Litz, running a twist rate that gives a predicted Sg of less than 1.5 simply means you won't be getting 100% of the intrinsic BC for that bullet, due to a slight increase in pitch/yaw as the bullet exits the bore.
However, that doesn't mean the bullet isn't stable. Typically, a twist rate that gives a predicted Sg of ~1.1 (or less) is where you might expect to see bullets starting to keyhole at the target. So that leaves a range of predicted Sg from around 1.2 or so, up to 1.49, where you may not be getting 100% of the intrinsic BC, but the bullet will be gyroscopically stable. I had an old Sig 556 DMR that was listed as having a 10-twist barrel. Using the cleaning rod measurement technique, it seemed as though it might have been a bit faster than a 10-twist. Regardless of the actual twist rate, it stabilized 77 gr SMKs just fine. I probably wasn't getting anywhere near the full BC, but the bullets weren't creating oblong holes in the target or keyholing. So you may have a few more options than you think.
As a general observation, with your 10-twist barrel, you will still be at a disadvantage for F-TR competition in terms of the selection of bullets available to you. If you shoot where there is much wind at all, a 69 gr SMK load may well behave as though you're shooting a precision shotgun. Having said that, there are probably other bullets worth trying, simply to determine whether they can be stabilized sufficiently in YOUR 10-twist barrel. Berger's 73 BT bullet is one possibility that comes to mind, Hornady's 75 BTHP would be another. If your barrel is really spot on 10-twist, chances are that neither of those bullets is going to give stellar results, as the twist will be too slow. Nonetheless, they might be worth a try.
Probably the best advice you've been given so far is from natdscott above. Can you shoot a 69 gr (or less) bullet weight in F-TR at 300 to 600 yd? Of course you can. However, knowing that they are at a big disadvantage in terms of wind deflection might be pretty discouraging for some people, so you might be running the risk of losing interest in a sport you might otherwise enjoy, simply because of the inherent limitations placed on you by using such a slow twist barrel. As long as you are aware of the limitations of your barrel and still want to compete, you should definitely have at it, even if only to have fun and learn a little bit about F-Class competition. So any experience you gain will not be wasted. The good news is that all you need to do to fix the issue is to replace the 10-twist barrel with a 7-twist barrel, throated for 80-90 gr bullets. Obviously there is some cost involved in that, but it shouldn't be too painful (i.e. not like having a new rifle built from scratch). You can obviously do that at any point, particularly if/when you decide the 10-twist barrel is a limiting factor. So as long as you go into this with open eyes, it shouldn't be a deal breaker.