I use 2ml and 5ml tubes for storage, and although the tubes themselves have a labelling area that will take a pigment based ink and is large enough to take the whole number if the pen tip is fine enough, I too find it awkward to write the large number. I settled on temporary numbers that go on the lids, to be later augmented with “in tube labels” printed with laser printer. My temporary numbers now are a letter for the site/visit, with 2 digit number after eg C24. I seldom collect more than 100 specimens per site, but could do 3 digits if I did. I try to get photo in situ, then photo the tube number it gets put into. When uploading the obs, I get the number from the tube photo and put that on the observation as a tag. Once the observation is IDd etc I enter the details into a spreadsheet setup with the labels, and when the sheet is filled I print and cut out the labels. Then I just go through and insert each label into the appropriately numbered tube. Sometimes I delete the temporary tag number from the observation, but other times not. I also started putting a tag to indicate that it was in my pinned storage, or for alcohol stored specimens I would put the actual storage box, eg “blue box”
It does pay to test the printing to make sure it holds up in alcohol… notice that the hand written label is wearing off, and in this case I was using the whole iNat number, broken into two parts. I don’t really see the need to the numbers being sequential, but I do find it helpful to have them in increasing order, so that each number corresponds roughly to a chronological progression. The great thing about this is I can pick up any tube in that blue box, go to any observation in iNaturalist (even not my own) and just replace the iNat number at the end with the number on the tube, and I have access to the current status of ID on that, as well as any conversation that has occurred on it… it literally becomes the field notebook and collection record all in one place!
This is how the labels look in the spreadsheet, and I double check for new or changed IDs before printing. The temporary label number gets cut off when inserting into the tube…