Yes, I'm double counting, but that hardly makes a difference (13% vs about 2%).
It actually in many scenarios it will make a significant difference because the lower inflation number is applied to the majority (hopefully) of your spending so smaller changes in that number will have an outsized effect on overall spending growth.
It's going to be more than CPI, simply because each year we're one year older.
I've never though of this as part of inflation, but you're certainly right that every year you're statistically more likely to need more healthcare than the year before. I haven't tried to put a number on that before. I found this paper* which claims the average 20 year old will consume $1,448 in healthcare spending, while the average 85 year old will consume $17,071 dollars.** That works out to a CAGR in healthcare spending of 3.86% independent of (and on top of) overall healthcare cost inflation.
Now that's a bit pessimistic because it is looking at total medical expenditures, not out of pocket spending. The ACA has a lot of wealth transfers from healthy young people to less healthy older people built into it, which slow down the rate of out of pocket spending growth relative to total healthcare expenditure growth by raising your total spending when you're young, and lowering it when you're old. And of course after one ages out of ACA and into medicare, a big chunk of the total costs are picked up by the taxpayer (or by your own previous medicare tax payments if you prefer), but either way aren't being paid out of your stash.
Now regular healthcare cost inflation has been running 2-5% in recent years when regular inflation was 0.5-2%. So I think one could make a reasonably convincing case for inflating the cost of healthcare in your simulation by as much as 7% above base inflation (up to 3% inflation premium for healthcare above regular inflation, plus up to 4% annual healthcare spending growth from being a year older each year).
*
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1361028/** I should also mention these are inflation adjusted 2000 dollars, so the numbers would be higher today, but the ratio between the two is the same.
I used 13% and got an answer that was pleasing. It seems sufficiently conservative, some would say ridiculously over the top, but it works for me (the stash is big enough) so it's not an issue. YMMV.
I think this statement is a good example of the root cause of many disagreements about the 4% rule. You've got more than enough money given regular assumptions, so when you do the math you're trying to to figure out how crazy things can get and you'd still be okay. In your shoes I'd probably do the same thing, because it seems like it would help a person sleep better at night. Others who are still in the accumulation phase are often just trying to figure out what a good set of regular assumptions to use are.
The first task obviously calls for a much more pessimistic set of assumptions than the second one, yet people mix the two discussions together without usually specifying which task they're currently working on themselves (although in this case you did explicitly explain what was motivating your assumptions, which was quite helpful, thanks).