Based on the molar mass, the factor should be 16.81 (do tell if I picked the wrong molar mass or something!). So by my count your values in mg/dl are 8.07 and 6.89.
0.41 mmol/l is well within the normal range but the normal range is irrelevant. The value is still too high for a gout patient which means the allopurinol dose should indeed be increased if you are tolerating it well.
Since you’ve had high uric acid for a very long time and just started allopurinol, dissolving crystals could well be propping up your test values. In that case, test values would trend down over time even if you didn’t change your allopurinol dose.
In my experience, test values can have a lot of noise in the 0.3-0.5 range even when you aren’t taking drugs so I wouldn’t make much of a single valu and I think you need more than two tests to know what’s really going on.
A warning: increasing your allopurinol dose quickly could also temporarily increase your risk of going through a violent attack. It’s for a good cause because in the long run you’ll be better off for the dose increase. But be prepared.