Rubbing the area where you shoot lantus is not good. That is because of that lantus depot. Lantus forms a microcrystalline structure beneath the skin in the injection site area. If you are rubbing or massaging the injection site, you are disrupting that microcrystalline structure and you may be causing the insulin to release faster.
You want those crystals to dissolve on their own, slowly releasing the insulin. It's what gives lantus it's nice long duration and gentle curve.
Yes, please stop rubbing the injection site to "diffuse the shot."
Lightly running your hand through the fur to check for wetness is ok. But please don't rub or massage the area.
"insulin glargine has an isoelectric point of pH 7, which renders the insulin molecule soluble in acidic solution (pH 4) [
84]. Upon SC injection, the acidic solution is neutralised leading to formation of microprecipitates from which small amounts of insulin glargine are continuously released to the circulation"
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6079517/
"Soluble insulin that does not precipitate in the SC tissue will diffuse and increase in volume upon SC injection, resulting in depot dilution. The relative increase in depot volume and consequently depot dilution occurs faster for small- compared to large-volume depots [
34]. Smaller depots will also have a relatively larger surface-to-volume ratio that increases the diffusion area of the injection depot [
101]. The result is a relatively faster absorption with smaller injection volumes"
Relevant to the large dose of insulin you are using, that larger depot will have a slower absorption rate.
Proper injection technique with large doses of insulin are also important. So that the insulin dose does not leak back out after injection. Just as you would hold an insulin pen for 10 seconds before withdrawing it, you may want to consider using that same technique with large insulin doses. See table 4 in this document from 2018
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6079517/