I'll try to respond this since most people have enough of a life to not be on boards on Christmas Eve (actually my kids all arrive tomorrow). Let me start at the end and do the questions.
1. Does what I'm trying to do make sense or have I got all this wrong? No, you're right, or pretty close. An IRA can be used to buy rental properties.
2. I saw in some posts that folks say using SDIRA for rental properties is not really worth it -- ...? One constant about investors is that you can ask any 2 and probably get 3 opinions about any given subject. Yes, some say it's not worth it. Others use it. Diff'rent Strokes for Diff'rent Folks.
3. Can I buy properties with putting a partial payment down and getting the remainder financed -- ...? In theory, yes. In reality, maybe. It requires a 'non recourse' lender. In other words you can't use your credit to stand behind the loan. There just aren't that many lenders interested in this area. I wouldn't count on it. One other point -- financing within the IRA opens you to an extra tax called Unrelated Business Income Tax (UBIT). It's one of the reasons that figuring out how to make money with leverage in an IRA is tough.
4. I've seen some heart burn regarding Managing Property bought through a SDIRA ...? This is a gray area, and one that's fraught with uncertainty, even among professionals. Some say you should hire a property management company. Some say managing it yourself is fine, just don't allow 'sweat equity' to disqualify your whole deal. A rule of thumb that my adviser gave me was to never do anything that you've seen in a MLS listing. You see 'Freshly Painted' in the MLS so you don't do that. You never see 'Carpets Freshly Shampooed' so that's OK. This is murky to say the least.
5. Let's suppose I've used up all my money to buy a property and there is an emergency repair ...? Major issue. You have no recourse except to wait until you can get some cash legally into the IRA. Make sure you have sufficient reserves if you do this. Reserves are your friend in a SDIRA.
6. A variation of the idea ...? Technically, this may work. But it will never happen. Getting financing in an IRA is pretty difficult, and then you're going to get hit with UBIT to pretty much take the profit out of it.
My opinion is that it's not a bad way to do things, but don't expect to be able to get borrowed money in play. It may happen, but there are few lenders, it's expensive, and it must be accounted for correctly.
One more thought: If you have $130k to put into a SDIRA now and can toss in an average of $6,000 / year over a 20 year horizon then you can probably get to the 5 properties level without leverage (depending on assumptions of growth). Especially if you can throw off $1,000 monthly from the rental and add $500 from your pocket. Playing with a spreadsheet may be in order. Just a thought ...