Tax help for military filers

Having served 20 years and being from FL myself, I can help you understand this.

Having recently made my first PCS move, I made the mistake of claiming my state of legal residency as my currently stationed state (GA), and did not know that I could claim FL as my state of legal residency because of being commissioned there as my home of record.

Based on the information you've provided, FL is not your HOR and never was. Here's why, based on your comments.

• I lived on-campus all four years of my FL university.
  That doesn't make you a resident of the state. Thousands of out of state students live on various college campuses in FL, yet are still required to pay taxes in their home state on all of their income, including income from a job they may have worked while attending college in FL. So this means nothing for establishing residency in FL.
• All my taxes were filled in PA for the four years. My additional scholarships were earned through taxable university income by my school.
  Scholarships and grants are not "earned" any way you look at it. They are "awarded". But you reported that income on your PA state return, further substantiating and affirming your PA residency during the entire four years of college.
• I kept my PA drivers license throughout my time in FL, and continued to vote absentee ballot to PA while in Florida. 
  So this even further substantiates that you are not now and never were for even one single day, a legal resident of FL.
• While I am leasing a vehicle from FL, it is still titled and insured through PA.
  That just further substantiates you had/have no intention of changing your state of legal residence from PA.
  I have been trying to figure out SLR so that I can quickly change my title and insurance to the respective states. 
  Titling a car in FL holds no weight for residency. You can title your car in any state you choose.  Insurance is another matter though, since you're military. It depends on your insurance company. For example, for AD/MIL in some states, for your insurance to be considered valid by that state, it *MUST* be purchased through an agent that is licensed in the state where you are stationed for more than one year. Hawaii is one such state.  So check with an agent in the state where you are presently stationed via PCS orders.

I do not own any FL property. 
While property ownership in FL is not a de-facto requirement, it most certainly helps. But for you it would be completely irrelevant since you filed state tax returns for PA. Another big factor for you is that you never filed a "Declaration of Domicile" while you were physically in Florida.

A Florida "Declaration of Domicile" is a document which allows you to declare that you are a bona fide resident of Florida because you reside in and maintain a place of residence there. You intend to maintain the residence as your permanent home.

You must declare in the document whether you maintain another place or places of residence in some other state or states. If so, you must confirm that your residence in the State of Florida constitutes your predominant and principal home.

The Florida Declaration of Domicile must be signed by you in front of a notary public or the deputy clerk of a Florida court. It must then be recorded in the public records of the Florida county where you reside. There's a minimal fee for recording.

The penalty for perjury for falsely signing a Florida Declaration of Domicile is five years in state prison and a $5,000 fine.

Although signing and recording a Florida Declaration of Domicile is not required to establish your Florida residency, it does put the public on notice that you have indeed made Florida your permanent home.

This document is filed in the county courthouse of the county where you have established your residence. Since you stayed on campus all four years, you never established a residence domicile in FL and therefore filing a Declaration of Domicile would be fraudulent anyway.

The finance department stated I can change my SLR at anytime.

Yes you can. But that doesn't make it legal. If your W-2 shows anything other than PA as your HOR you could have a problem down the road since you never established residency in FL. If PA finds out about this, they can (and will) come after you for back taxes which will include fines, penalties, late fees and non-filing fees. Since you did file tax returns with PA during your college years, it generally takes about 24-36 months before flags are raised from them not receiving any tax returns from you for the prior 2-3 years. That's when they come looking for you and they will find you. Being military I can tell you right now they will find you through channels; i.e.; your chain of command. The last thing you need as a commissioned officer is to be called in by your commanding officer for an explanation. When that happens (and it will) you can forget about the next promotion cycle...you won't be in it.

I know I'll need to file for taxes in GA anyways because of my error,

No, you do not need to file taxes for GA. But you do need to get with the base legal office to find out the procedure for getting any taxes you paid to GA, refunded to you. But at this point in time, this is the least of your worries or concerns.

is it still feasible to legally claim FL as my SLR?

No, not by any stretch of the imagination.

I understand that an educational transcript can count as proof of residency,

Sorry, but that's not true. Just flat out no, it doesn't prove residency in any way, form or fashion. All it proves is where you attended college, and nothing more.

not sure which can or would be the second form of proof of residency for a driver's license.

Based on the information you provided in your post, the only residency that you have proven beyond any doubt, is PA residency. You really need to file tax returns for PA for all the years you didn't after finishing college.  The good news is, though you may be required to report your military income to PA, it may not be taxable. According to what I read at https://www.revenue.pa.gov/FormsandPublications/FormsforIndividuals/PIT/Documents/rev-612.pdf

Military pay (including compensation for weekend drills) earned within and outside Pennsylvania by PA residents is subject to PA personal income taxes compensation. Income received by a PA resident for all military service performed inside Pennsylvania – even if on federal active duty or federal active duty for raining – is fully taxable, unless for active military duty within PA for an emergency pursuant to 35PA C.S. Ch. 76.Military pay received while on federal active duty or federal active duty for training outside Pennsylvania is not taxable.