I am open to trying what you do with the higher price on one of my properties just to test it.

How should I phrase my interest in the property to avoid coming across as pushy or insensitive?

If you want to stay in your house, then your only option would be to leverage equity which will probably be in the 8-10% interest rate range.Not knowing the entire situation, I think you could consider downsizing and then using the proceeds to buy a 2-4 unit property and start making $40-75K right away with still no debt. 

ADU construction is not 1:1. meaning investing 250k into your property by ADU will likekly not increase your property value by 250k.

I am based in New Zealand and own 4 properties here, but keen to explore investing in the US. 

For example the HA will inspect the property every year to make sure it is up to standards. 

I'd keep an eye on ancillary properties that become available. 

Has anyone added extra bedrooms to a multi-family property to increase rental income?

I have been an investor for over a decade and helping other investors (many OOS) buy and sell investment properties here in the Dallas/Ft.

I have been going through this thought process recently running some numbers to on a few investment properties for my wife and I.