One thing you mentioned in the OP was you’re going to “relight” a fire and see what happens. Are you not burning 24/7, then? Nothing wrong with that, but, I have found that my Napoleon 1101 (1.7 cu ft box) can maintain the house around 72 much better if I burn 24/7. If you aren’t burning 24/7, your home is going through drastic temperature fluctuations and your asking your insert/stove to pull that weight.
Also, are you immediately closing the air supply down? You may try going down in stages instead of dropping all the way down right away. Your fire may not be burning hot enough to get secondaries if you close down too soon. And then by time it is hot enough, all the smoke (for the secondaries) is gone because it’s too late in the burn phases.
Wood species is almost irrelevant. BTU May be higher on hardwood/deciduous species but there are plenty of guys in here, myself included, who can heat just fine with pine, fur and cedar. Making sure the wood is properly seasoned is WAY more important.
Also as Freddy said, insulate and seal. It did wonders for me. Dropped my electric bill another 30 per month on a budget plan once I have had the chance to look back on two years worth of bills. With and without the upgrades. The additional $30 per month is in addition to the several thousand dollars I’ve saved since I started burning, 7 years ago.
These are just my humble opinions