A stock White Paint will not provide enough gain for 3D viewing at the size screen & PJ combo you have.
Don't try to take too simple a route here. It's a temptation to follow advice that seems to make sense "cost & effort" wise. But your self stated goals simply do not allow you that luxury.
You might be advised of this, and warned about that, coming from varied sources...but it is a fact that this Forum has had far greater success at achieving "above the bar" performance on really "BIG" screens (180" - 225" diagonal) using specific Paint applications on a variety of materials than anywhere else...using anything else.
Be serious about achieving your goals (...and then some...) and you'll get there...guaranteed. Waste some time following ill-advised suggestions and you'll quickly become more than a little disgruntled.
From what I already know and have read (here & elsewhere) your going to have to erase your own reluctance over trying a higher gain paint formula, and ignore any derisive or derogatory comments you have seen...elsewhere. On this Forum we strive to help people and provide solutions. Some are very simple and inexpensive. Others are answers to more difficult questions, so they require more effort, and expense.
Guess what? You fall under the latter category. Would that it be different for you...but it's not.
You'll need a primarily White based paint...one that does (Gawd help ya!) contain considerable reflectivity via the use of Mica. The base will be 2 parts Flat White Enamel (FLAT !!! NOT SATIN !!!
) and 4 parts White Pearl, and 1 part "Satin" Clear MinWax Polyacrylic . To that Mix, fully 3 parts Distilled Water is added....very well mixed
This is a Spray-Only Top Coat application, laid down in successive light coats over a very smooth surface.
This Formula can easily receive a basic Gray Tint by adding any prescribed amount of Liquitex Basics Neutral Gray. Just a little dab or a nice dollop. Either way...the amount of metallic in the mix, effectively muted by the White Enamel, but also augmented by the Polyurethane/water creating a deep, semi-translucent surface is what will provide you both the gain you need and whatever degree of slight to maximum contrast enhancement your facing. And with the Z2000, you should employ a tinted N-shading of around 8.5 minimum.
So lets examine a few other items.
First off, your throw distance is not gonna work. 15' is the absolute minimum...and you don't want to be at the extreme end of that...so you should add about 10" to that measurement.
Secondly, at that throw and Screen size, on a 1.0 gain surface, the Z2000 PJ will at maximum
provide 8 foot lambert ...and even with a Dual PJ set-up, in 3D mode
(w/Filters) you'd wind up with just (hopefully) 3 foot lambert. You don't want to even consider such.
But up the Screen's gain to 1.5. Now you have 12 foot lambert x 2, for a estimated 3D foot lambert level of 9-10 foot lambert.
Then...there is S-I-L-V-E-R, whose degree of reflectivity can be adjusted from 1.4 up to / beyond 2.2 gain. That application has proven itself on 200"+ screen being hit with just 700 lumen (RS-1) from throws exceeding 25'. It's performance was so impressive on one 215"er, many who saw it in person speculated it might be well over 3.8 gain (...it was not...) and it even possessed enough "PoP" to present a decent, watchable image in low, controlled ambient light. But darn it! Your gonna have to spray that application as well.
That was over 4 1/2 years ago, a time when...you might well guess...some folks were still trying to discount the need and / or effectiveness of using Mica in a DIY Paint mix.
Now remember to consider that the images below are a 215" diagonal screen w/700 lumens...spray Painted with S-I-L-V-E-R onto a smoothed and sanded White primed Drywall surface.
When you see shots like the ones above, and read other postings about how such things are not possible, you have to use your own common sense as to where the correct information is really coming from.
So it's time to choose. Go for a speculative "Hope & Promise" solution (ie: hopeless) that is absolutely leave you wanting...(btw, any stock white that is over 1.2 gain got there because of "sheen"...)
...or get down to choosing something that will accomplish exactly what you want. No time for, nor need for "Tit fr Tat". I certainly am not afraid of any adverse results if you stick to and follow some pretty basic instructions. And....it's not really gonna cost much...perhaps $130.00 including Paint and Sprayer.....even better, your NOT
gonna have to evacuate the House, and even if you want to...perhaps for 1 very long day under ideal circumstances.
You were /are a early AVS member who is at least hopefully aware of DIY Screen History and it's accomplishments, and can discern what facts might actually have merit, and what is simply someone pouring you out a drought of sour grapes.
Come back, stay...get something memorable accomplished, and drink the nectar of success.
OK...that's a little "over the top"...but in DIY Screen making, that's always a good way "to roll".
I mean "spray".