It is not very common for schools to match scholarship offers but definitely not unheard of.
There is a set pool of money I am not sure that the fin aid office is the one calling the shots - it is likely a joint or more or less purely adcom decision how the pie gets cut. Fin Aid office simply administers it. As the result, I would guess you would have more success reaching out to an admissions person (if you were smart enough to meet/chat one up/stay in touch with one) and start your process there. You would be much better served if you were able to get ad adcom member to lobby on your behalf vs. cold emailing an undergrad student worker at the financial aid office.
P.S. Adcoms do consider all admits as their "folks, people, and depending on age, sometimes children" so there is some attachment and there is some responsibility involved in that relationship so you don't need to feel like a stepchild - they are also interested in your success and your eventual matriculation. This may be something to save after the admit student weekend where you can meet an adcom member and establish a stronger relationship but don't wait long into R2 when money get scarce.