That's easy to fix.
Unless the tank is full or close to full, the backflow isn't coming from the tank, it's waste in the head discharge line that isn't making to the tank. The fix: install a loop--not a vented loop, just a loop--in the toilet discharge line immediately after the toilet that's slightly higher than the top of the tank. Then all you have to do is flush long enough to push waste over the top of the loop. To prevent what's left in the line between the toilet and the top of loop from running back to the toilet, learn to use the dry mode to do more than just push the last of the water out of the bowl. Most people don't realize that any toilet that's working anywhere near factory specscan move bowl contents up to 4' IN THE DRY MODE. This does require a joker valve that isn't worn out (see the article "joker valve 101" in the archives of the plumbing and sanitation forum and my book to learn the joker valve's REAL function, which is much more important than just blocking backflow)...so after you push the "deposit" over the top of the loop in the dry mode, switch to wet to bring in some flush water to rinse behind it...then switch back to the dry mode to push the rinse water over the top of the loop. This not only will cure your backflow problem but has the added advantage of reducing the amount of flush water enough to increase the number of flushes your tank can hold by at least 50%.
The following applies to ALL toilet installations, no matter what route the plumbing takes: If the "deposit" will be solids, add about a quart of water to the bowl ahead of use. This will keep the bowl clean and require much less flush water to move the flush to the tank. If your toilet isn't designed to bring water into the bowl and hold it there, use water from the sink...two 16 oz Solo cupfuls.
A little more effort, but a LOT cheaper than replacing the tank and all the plumbing.