My question is this "If my current 403B allows it, would it be feasible to "roll over" both of these in order to avoid being subject to taking a Required Minimum Distribution from them prior to my actually being "retired"?===========>>>>>>I guess you need some professional help form a retirement plan admin however, I guess yes you can in your situation; providing the 403(b) plan permits such rollovers. Since you are still employed by the 403(b) sponsor/ER, you need not take RMD amounts from the 403(b) account until you retire. If you rollover your traditional IRA/TSP to your 403(b) account, the IRA amount will be subject to the same provisions. Only the pre-tax amounts held in the Traditional IRA can be rolled over. Any after-tax amounts in the traditional IRA cannot be rolled over to your 403(b). The sources of after-tax amounts are nondeductible contributions to the IRA and rollover of after-tax amounts from qualified plans and 403(b) accounts.
NOTE; the IRS prohibits tax free rollovers of amounts that are subject to RMD in the year in which they are due. You cannot use rollovers to avoid taxes on RMD amounts. Instead, you must take the RMD in full, or risk a penalty of 50 %; so aslongas they are subject to RMDs then no.
My limited understanding of my 403B is that RMDs would not apply as long as I was employed at the institution that I have my 403B with. ===========>>If you are participating in the retirement plan where you work and if the plan allows, you do not have to take any RMD from that plan until the year you retire. Rmd is not required if still working past even 70.5 .rmd must commence upon subsequent severance from employment, regardless of age. Still working/ be employed" means you have not retired from the position in which you were covered by the 403(b) plan; also keep in mind that the "still working exception" applies only to a current employer's retirement plan and does not affect IRAs , tsp, or retirement plans ,i.e., SEP or etc established by those who do full- or part-time self-employment work. I mean once you reach the year you turn 70 ½, you must take an RMD. You also have to take RMDs from any employer plan if you are no longer working for that employer. The “still working” exception only applies to your current employer.
Note; your 403b plan, aslomfas the required minimum distribution requirements for pre-1987 contributions to a 403(b) plan has separately accounted and kept records for pre-1987 amounts, and is for the primary purpose of providing retirement benefits, then, the pre-1987 amounts (excluding any earnings or gains on such amounts) are not subject to the age 70½ RMD rules ;are not used in calculating age 70½ RMDs from the 403(b) plan, and don't need to be distributed from the plan until Dec 31 of the year in which a participant turns age 75 or, if later, April 1 of the calendar year immediately following the calendar year in which the participant retires .