What you linked and copied applies strictly to "losses" not gains. You mentioned that for a 40% abv spirit you can be from 39.85% to 40.15% and that's not correct. For a 40% abv spirit you have a tolerance range between 39.85% and 40%. Period. You cannot have more spirit in the bottle than what is stated on the label. You must correct the stated abv on the label (which doesn't require a new cola) or properly proof your spirit to the tolerance range.
The TTB is interested in maintaining proper tax influx. By under-proofing your spirit you are, in effect, sending 1% abv of untaxed spirits out the door (using op as an example). The TTB recognizes that losses occur to proof through the bottling process and have given a tolerance range that accounts for that, but you must not have more liquor in that bottle than is stated on the label.
The best way to assure you're proofing properly is to take your time. It takes me 5-10 hydrometer readings (depending on the volume being diluted) and ample time for agitation/diffusion to make sure we are accurate. I want the proper amount of liquor in as many bottles as possible, as does the TTB. Don't give away spirit for free (or without taxes paid).