I have a Ruger American in 5.56 and I'm trying to mount a 40mm obj scope that isn't a mile above the bore.  Due to the built in pic rail above the action even "low" rings sit the scope a good 8-10 mm too high

Anyone have recommendations on a decent set of low (er) rings that won't sent me back $150?

I have come to like Leupold QRW rings, a they are quick to detach, quick to re-mount, and will hold a zero when re-attached, properly. The main thing with the QRWs is that they will retain their guts after being detached, whereas some other rings will not.  Unfortunately, the QRWs are of steel construction, BUT they are not at all expensive, and very stout.

Whether Leupold offers rings in the height you require is up to you to determine.  One mfr's "low" rings might be higher, or lower than another mfr.  Most reputable ring mfrs will provide specs that can be compared by the astute buyer.

Concur in your desire to have the optics mounted as low as possible.  Doing so is seldom a bad practice, in my experience.

I got these for the same rifle with a Vortex Diamondback 4-12x40. I can measure when I get home to see if they meet what you want, but they were fine for me

No offense, but the rings you linked are NOT QD rings.  They might be excellent rings, but IMHO, are UNSAT because they are not Quickly Detachable (QD) in the event the optic becomes unusable for some reason.

I have come to appreciate the option of being able to quickly switch from an optics system to iron sights.  This option, IMHO, can be a very valuable option.

Again, no offense intended.

I know they’re not, OP didn’t specify he wanted QD rings, just low rings. Also didn’t see where OP was running back up sights, so not sure where the whole need for QD rings came up for a bolt action rifle when there was no mention of back up sights.

NO offense intended, please.  My suggestion was made in all good intent,and no insult to anyone.

I have lots of rifles, with many different types of actions.  One thing I always try to ensure is that the rifle has good iron sights (not always available, out of the box), and that the optics are mounted so that they can be quickly dismounted, and the iron sights be immediately used.  Likewise, the optics should be able to be re-mounted, with no loss of zero.

No doubt I am something of an exception, but I have no reservations about my personal practice. YMMV.

Some Leupold rings are on the way.

The Ruger American Rifle doesn't have irons so I don't need/want QD..

I'll report back once everything is assembled.

Meaning no offense, may I suggest re-considering your rifle not having iron back-up sights?  It is true that such are seldom required, but when they are needed, it is imperative they be present, sighted-in, and ready to use.  The ability of the optics to be quickly removed is a necessary prerequisite to be able to use the BUIS.

The ability to quickly remove/dismount the optics, and be able to use sighted-in BUIS is, IMHO, fundamental for most Riflemen

There are many ways to add BUIS sights to rifles lacking such.  May I suggest you consider doing so?

YMMV, of course.  

If it were a rifle that I would risk my life on, it would absolutely have backup iron sights, and it most certainly would not be a bolt action 5.56.

Most modern bolt action hunting rifles I've looked at don't have irons.

I have made a point of having Iron Sights fitted to my rifles that lacked such, sometimes at considerable expense.  Have  never regretted doing so.
Having a viable Plan "B" is very useful.

YMMV.