I read the TSB, but I did not see where it said the battery will not survive a full discharge. This is a very expensive battery, and I would not write the obit just yet.
The TSB has some information in it that can be misinterpreted. It says you should not charge the battery at 2 amps. The only reason is that you would not want to pay Toyota to charge it at 2 amps. Would cost you a fortune. Technically there is nothing wrong with charging at 2 amps other than the time it takes.
The TSB says you should never charge the battery with a standard battery charger. Yes, you should take it to Toyota and let them use that special charger and charge you $100. Nonsense. I'll bet 9 Toyota shops out of 10 will use a standard battery charger, probably harm the battery, and still charge you $100. The only thing special about the battery charger is to ensure you use one that delivers 5 amps or less. Yes some larger chargers will deliver a lot more, and if you use one of those set to a high value, you will likely destroy the battery.
It is worthwhile to keep the theory in mind. Toyota uses a special battery to avoid gassing when it is charged, because the battery is located in the trunk. You don't want explosive gas in the trunk. I believe they originally used Gel type batteries. The gel absorbs the gas generated, providing you do not charge it too fast. If you charge it too fast the gas forms bubbles in the gel and the battery is ruined.
I suspect they now use AGM type batteries, but who knows for sure. AGM stands for Absorbent Glass Mat. The purpose is similar in that gas is absorbed. You are buying a black box when you buy from Toyota so who knows what you really get. AGM are more tolerant to faster charging. It is possible they set the 5 amp charging limit when they used Gel type batteries and have not changed it. In any case if you stick to that maximum charge rate you will not damage the battery.
See this link
, if you want to learn more about Gel and AGM batteries.
My recommendation to the OP is still the same. Get an inexpensive 2-5 amp charger at Walmart and recharge the battery slowly. If it does not recover then buy an Optima AGM type battery, and use that charger to fully charge it before you install it.