Well done for keeping your HbA1c at 54!!! I have no experience of weight-reducing-medication. However, I would suggest that you keep an eye on any side-effects, if you decide to start the injections.
Since you are eating low carbohydrates, that would mean correspondingly low amounts of insulin. So what is the reason for "upping insulin"? Unless you are having larger carbohydrates/insulin ratios?
Are you also having lots of hypos? I am not trying to advise you because your Diabetes Team will do that. However, in my case, I put on weight if I have unusually high frequency of hypos. All the Dextrose and sugary drinks to correct those caused my weight to increase.