Hi and welcome to the forum! Speeding nominations up is what Upgrades are for, so no, I don’t see another option to accelerate.
Be aware that there is a strong distinction between “Upgrade Next” and “Upgrade” though - “Upgrade Next” is for the future, to pre-assign the next Upgrade you earn by reviewing, while the “Upgrade” button immediately assigns the Upgrade and proceeds with prioritizing the nomination. So if it’s “Upgrade Next” that you’re applying, be aware that it does nothing until you actually earn the Upgrade. You earn it by reviewing and subsequently earning 100 Agreements.
I do want to say that 2-3 weeks is entirely normal though. Not to be all “back in my day” 
, but for many major urban centers 2 to 2.5 years used to be the norm for non-upgraded resolutions. My current oldest are from March 2024, to give you a perspective. The speed of resolution for your area depends on many factors and can basically only be measured empirically (but if you think it’s dependent on your city population - no, it’s not just people in your city reviewing you but people in a much, much larger square). So we unfortunately can’t directly say what to expect, as even for the same area the range is quite wide right now.