Affordable integrated pure class A?

Assuming you meant 85db, not 85hz, you're correct that those are low efficiency speakers and will need plenty of power. It could be class A, but that would cost you a pretty penny, for sure, especially if you go tubes. If you are on a modest budget, considering easier to drive speakers will make things much easier on your amp choice. 
FWIW, I have 85db Sound Lab electrostatics and also love the sound of many class A amps. I spent over $3k on a used Krell FBP-300, which is a fraction of the cost of other tube amps that I used with the SLs previously. At 85db, you want to be pretty committed to the speakers, as I am, knowing that amp matching will always be important and relatively expensive. Cheers,
Spencer

A really great sounding inexpensive integrated is a Tandberg TIA3012.  It’ll set you back $300-350 and is heavily biased into class A as it runs very warm to the touch.  I had one for a few years and loved it.  Kept it on all the time with about 4-5” of ventilation on top.  100 wpc, MOSFET outputs, very warm and tubey sounding.  I would take one anyway over NAD or many others mentioned.  Only sold it to go to separates.

Looks like I'm a little late to the party, but might I suggest trying to find a Yamaha R-9 receiver? It has a front-panel button for 'Auto Class A', which gives you about 30 watts of beautiful, pure Class A power (about 15 w/ch), beyond which it seamlessly transitions into Class A/B mode up to full rated power (conservatively rated 125 w/ch into 8 ohms, 20-20kHz @ .015 THD).

I've had an R-9 since new, bought back around 1985. The R-9 was Yamaha's flagship receiver, and I've never had the slightest problem with it - built well, and still looks and works like the day I bought it. Currently, my main system's preamp feeds the R-9 to power four sets of indoor and outdoor speakers around the house.

The R-9 is especially great if you have speakers efficient enough to keep the amp running in Class A mode most of the time - even those who aren't big Yamaha 'Natural Sound' fans say that the R-9 in Class A mode is a totally different animal. (Just be sure you have good ventilation, or even a small fan - 'Auto Class A' kicks off enough heat to fry eggs on the top of the receiver!)

From my experience, the R-9 was a very good, solidly built receiver that just never seemed to get enough respect, especially given its fairly unique Class A capabilities. A quick check on eBay shows several fully functional R-9s going for prices between $75 and $200, although one described as "fully restored" was priced around $1300.

A decent R-9 might be a good way to get your feet wet in the "Class A waters" without a mid four-figure outlay. If desired, you could then make a more confident investment into one of the more expensive alternatives, and easily resell the R-9 for whatever you paid for it.