I don't know what you do for work, but I have seen individuals use a large nest egg from real estate to start a business and change their life trajectory.

They will do the price shopping for you and find the based vendor based on your requirements. 

Realtors are required to bring all offers so by all means feel free to make an offer. 

I'll try to be helpful and concise here without being too long-winded...ESPP - Typically you buy this at a discount (Usually 15%) typically you get beneficial tax treatment on the discount and won't have to pay income tax on it as long as you hold it for their required holding period.

Along with the FHA loan, check out the loan from the Neighborhood Assistance Corporation of America (NACA).NACA was formed in 1988 and provides an affordable option for potential first-time buyers:✅ No down payment✅ No closing costs or fees✅ No mortgage insurance✅ No consideration of credit score✅ Below market fixed interest rateThere are several requirements to be eligible, starting with attending one of their workshops.https://www.naca.comI wish you all the best.

i.e. if you had a $190,000 hard money loan on House 1, you'd be able to get 80% LTV no problem with no seasoning requirements as rate-term refi

You may consider looking for seller's that will consider seller financing that may not require as large a downpayment. 

In addition to numerous tradition RE related investments (most individually owned but some as LP), here are our unusual investments (both are RE related, but not what is common on this site)- I have mentioned this one a few times on BP, when fracking was just starting to be known to the general public (near turn of century), we purchased mineral rights in North Dakota.  

Note that the difference between earning 10% in a fund and 12 to 15% from individuals is not 2 to 5%, but 20 to 50% on a cash returned basis.Most of the lenders we know who loan their own money and don’t find their own borrowers like we do, keep their pipeline full using brokers who bring them their loans.

Would it require you to change your lifestyle?