Buying Out of State Primary Residence While Renting Current Home

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Hello, Trying to see if someone has done this before and has any tips and tricks or ideas. I am currently living in a house that I have a mortgage on in MN. I have rehabbed the place nicely, but wish to move to Boise, Idaho about a year from now. I hope to keep this home and rent it out while I am living in Boise. My hope is to use a conventional/FHA 3% down loan for a property to either househack or have a cheap mortgage in Boise. Looks like the bank in Idaho will not give me a loan due to my job being in MN. From what I have discovered, I will need to rent in Idaho for a few months and establish having a job there for a few months while also having the MN house rent out for a month before the bank will count its income. I realize what I am asking may not be possible, but, is there any way I can get an FHA/Conventional 3% loan while they count my current home's rental income before I move out and count my job in MN as income? I will still be getting a job in Idaho once I get there, but I would rather avoid the renting for a few months and moving twice.... Cheers! Nick