The equity is actually what you are paying for the property.In this case let's look at the numbers that count,...the current numbers.You have about $500k or more in equity, which is buying you a property that's worth about $700k (I went with the lower PV. 

., obviously the barrier to entry is different but so is the ARV.

I have lowered the price significantly this year. 

I understand I cannot legally require them to respond, unless the notice specifically requires it, like for instance, a notice of entry, but it's making it difficult to manage the property, and I'm not sure how to proceed.

As a result, my DTI ratio is now greatly reduced due to this calculation method and my lower income.

You will want keyless keypad entry for sure.

This included some landmark deals including Rockefeller Center’s $3.5B loan and Miami Beach’s Fontainebleau $1.2B refinancingAlternative lenders filling traditional banking gaps with short-term solutions which has already begun a cycle of consolidation that will likely continue and accelerate in 2025The Office Sector Divide:CBD property values are down 50.7% from 2021 peaksClass A office properties seem to be in their own vacuum of prosperity with trophy properties commanding premium rents ($100+ PSF nationally, up to $247 in top markets) with strong occupancyHybrid work continues impacting older building valuations which have not faired as well, but this may begin to rebalance as more companies are instituting mandates to return to physical officesChallenges & Opportunities:$1 trillion in loans maturing by 2026Interest rates up from 3.5% (2021) to 6.74% (2024)Experts such as AEW’s Michael Acton and Blackstone’s Nadeem Meghji see the best entry point in the last 15–20 years and we agreeMarket Outlook:Current market conditions present unique opportunities, with inflation-adjusted prices at historic lows and yields at decade highs.

Question: Should I collateralize the loan (if using private or hard money), or rely on roll-over loans (to maximize the lower points and 3-4% rate)?

As you suggest lowering down payment to buy more properties is one way, although the downside is greater risk in event of down cycle and more time to manage required.  

The good news is that there are still investable vacation rentals but historically the barrier to entry is growing each year.