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BQ24040: intentional TTDM with large battery

Other Parts Discussed in Thread: BQ24040
We've got a product that's wall-power-optional: we recommend running it plugged-in, but our inclusion of large battery means we'll sustain periods without, potentially long periods.  We plan to refine/optimize our software (specifically, its radio usage) to ultimately run from it from battery, with infrequent re-charge.  The ability to recharge reliably becomes pretty key.
Sadly: Due to some design oversights with our contract EE, our large battery (1S6P, 15.6Ah @ 3.7V) is entirely too large for our BQ24040, so we generally run out of charge timer long before charging completes, even with ISET dialed to charge ASAP.  It's a poor-enough UX to ask the customers to unplug/replug to keep charging, but we've also seen that charge-timer expiration means that OUT goes dry and we discharges the battery, despite being plugged in.  The proper fix - replacing the part - is difficult because we're a young startup and not in a position to spin the boards.  So we've been exploring our options, like artificially limiting/monitoring our battery capacity to ensure we can always charge it in the window afforded.  we're leaving capacity on the table.
By coincidence, a manufacturing-time problem left a resistor populated between Vin and TS. This has tied TS high (~ 2.355V), so we've discovered TTDM, solving our timer problem!  But we know TTDM has other implications, and at a minimum mistreats the battery.  We've got backgrounds mostly in software, our contract-EE is cagey (doesn't know), and we know there're things we don't know about Li-Ion chemistry and the BQ24040, so aren't sure if those other implications are potentially more-serious, or are something we’d be willing to tolerate.  For instance: this is a product iteration whose life will be relatively short-lived. “it’ll take a year off the battery life” is probably fine. Of course, more serious thermal events aren't ok.
We've talked to a battery-expert fellow-entrepreneur who thinks - given the regulated 4.2V output, that we aren't using the product in harsh conditions, that charging goes normally overall (besides that it doesn't stop charging), that we're using software to detect/prevent it from getting it down to under-charge levels, that our software reports battery voltage telemetry,.. he suspects TTDM isn't dangerous, more a risk of shorter battery life - well within our tolerance.  Of course, our fellow entrepreneur concedes he doesn't know the chips, so can't answer very conclusively about what else TTDM implies.
We're interested in more opinions.