I have about double $80K actually, in cash, just sitting in a high interest savings account until I figure out what to do with it.

Yes - you should be able to find some good DSCR Loan Options with 20% down easily - 15% down potentially available but the rates/requirements are pretty high on that front right now

Purchasing a new primary and turning my current house into a rental and looking to hire a PM but some of the fee's seem high. 1 quote - 100% 1st/month rent if i self-manager, or 75% 1st/mo rent and 10%/mo for PM to manage.Again, im new to this but from reading and talking to people there is a typical finders fee ~1000$ and 10%/mo rent if the PM manages. 

Given your residency limits, the high prices in NYC and surrounding areas are a challenge, but there are still options in neighborhoods further out within your allowed range, like parts of Queens, Brooklyn, and the Bronx.

My sister recently moved to HI, and I figured that might be an interesting market because of high rents and HCOL - although also high property values.

We paid ours off when our balance was $125k, but on a 15 so payments were fairly high at $1732 PI.

We respond to inquiries, but if someone did the things you suggested to try to track me down instead of following the advertised protocol I would disqualify you as crazy or a potential stalker or just high needs or high maintenance. 

Doing that using the BRRRR strategy right now is highly unlikely.

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Mortgage lending is highly competitive, and there are many newbie loan officers that will bend over backwards to get you to pull a credit report and pay for an appraisal.