I don't think this is possible on many, if not most boats, especially if you want to keep as much way on as possible.
Then there are the boats with staysail stays that hamper swift tacking. One surely doesn't want that sail to fill on the wrong side of that stay so, patience is required. That means you've a lot of sheet needs to be pulled in after the wind has passed the bow.
One thing many new sailors do when they tack is to put the helm hard over at the beginning of the maneuver. Well, that's just like throwing out a barn door behind the boat and will quickly bring her to a near stop.
If you've been doing that, try throwing the helm over only as far as necessary to get the bow to begin to swing through the wind. It should make tacking significantly easier. Multihull sailors learn this PDQ, or they spend a lot of time in irons.
The OPs boat is 26 feet. That is the focus.
Yes, an inner stay is a problem. I've had one on every boat I've owned when I set a reacher up wind, an it is a problem. Your boat has one, is twice the length of the OPs, 5 times the headsail area, and over 10 times the sheet load. It is simply not a useful comparison in this context.
The best turn-in speed is certainly boat and conditions dependent. It is also common to increase the helm slightly as the boat slows and the turn proceeds. It is also important to match the turning speed to the speed the crew can haul the jib across. With F-24, for example, which can turn very quickly at speed, the determining factor in turn rate is often hauling sheets. No use turning the boat faster than they can get the jib in, it only results in flogging, more grinding, and a slower over all tack.
I have sailed multihulls for 4 decades, including a 34' PDQ cruising cat, and the best tacking methods was to turn relatively quickly, starting somewhat slow but quickening as the boat slowed, and getting the jib in JUST as it could fill on the new tack (about 25 degrees AW). At that instant there is still little load. The wind then grabs the sail, pulls the bow through the wind, and starts the boat accelerating before the turn is even fully complete. In fact, on a boat that can very easily go into irons, like my PDQ, it is the very best way. Backing the jib, on the other hand, only slows the boat, making it more likely you will find yourself dead in the water and pulled into irons than simply getting the jib in at the proper moment. Watch beach cats race and see if anyone (other than beginners) ever backs the jib. They don't.
And it does not require crew on boats up to ~ high 30s. The turn is handled by the AP, you realease the jib when it breaks and pull it across at the rate the turn allows. When you get it right, when the jib pops full the first moment it can and the boat is pulled around and accelerates, it's wonderful.