Appropriate charging current for parallel 18650 lithium cells

There could be some legitimate reasons why this won't work well. These may not apply to you, and if you review the documentation of your charger, you should be able to tell whether these things apply.

Probably you are aware that it is not safe to float lithium ion batteries at 4.2V indefinitely. Because of this, all Lithium ion chargers use some method of recognizing end of charge.

Typically, end of charge is determined by how much current flows into the battery. For a single 18650 cell, end of charge may be defined as the point where charge current drops to 25mA during the CV stage. But with 9 cells in parallel, it may never drop that low.

Which brings me to the second point. Timeout. Many charger IC's will not allow an indefinite amount of time for charge to complete. This is a backup safety in case a defective battery is present, or something else prevents the primary charge termination condition from occurring. Typically this timeout would be set to some number far larger than you would expect to ever happen unless something is wrong with the cells. On a C/3 charger, you would set it to 5 hours or 8 hours. If your charger has a feature like this, it could possibly prevent the pack from charging fully. You would have to remove the pack, and put it back in to restart the charge timer.

Again, without seeing your charger details, I can't say whether these two issues apply to you. But you may want to check it out or at least be aware and keep your eyes open.

Someone mentioned that the 1A max current simply would not work for 9 parallel cells

Nonsense !!! it will work but it will take a very long time to charge. One cell of 2000 mAh (=2 Ah) (a typical 18650 is 2 - 2.5 Ah) takes 2 hours to charge so 9 cells take 9 x 2 = 18 hours to charge. Close to a full day indeed, not all the energy ends up in the cells and is lost so in practice 1 day sounds right.

As long as I'm charging the batteries with more current than I'm drawing from them, they should charge, right?

Yes, that is correct.

Next time someone gives an opinion about things always ask why and ignore their advice if they cannot give a good explanation.

For your information, your charger is based on TP4056 chip, programmed to 1A charge current. There's no safety timer, meaning it will continue to charge until the charge current drops to 100mA:

Other than being slow, there are no apparent problems with your charger.