Seeing a picture of your progress would help tremendously. The way the question is worded, it sounds like you were wanting to drive the beveled gear directly from the servo to the rack at a 90 degree angle. This won't work for two reasons: 1. The majority of Lego racks are not beveled. 2. The rack moves fore and aft as it moves side-to-side, which would disengage the gears.
I threw together a rough, working rack & pinion setup with beveled gears to get a better understanding of the play you may have been referring to. You didn't mention which type of beveled gears you were using so I tried it with two of the most common types. My only 2 "PF Servo Motors" are deeply embedded in other vehicles at the moment so I used an "M" motor in it's place. Because of this I could not compare the two for "play" in the output shafts.
In both applications the majority of the play I observed was coming from the motor itself, not the gear mesh. I also don't have a clue as to how you built it verses the way I did. Because the gears and size of the assembly seemed to be your priority, I placed the motor in a more compact position. The orientation of the motor and which way is "up" can easily be modified per application.
The first test uses the "32270 Technic, Gear 12 Tooth Double Bevel".
The second test uses the "32198 Technic, Gear 20 Tooth Bevel" to drive, and a "87407 Technic, Gear 20 Tooth Bevel with Pin Hole" for an idler gear.
Both set-ups had very similar play, all of which appeared to originate from the motor. I did try the smaller "6589 Technic, Gear 12 Tooth Bevel" but it seemed to exaggerate the play. This is possibly from the lack of an idler gear and/or from the greater angle of the teeth, needed for the smaller gears to mesh. I therefore excluded it from "working prototypes." When comparing the "play" in the assemblies that I built verses the steering on my 2 vehicles with the Servo Motor (set# 41999 & MOC using 88004) there was no noticeable difference. In other words, I think this is as good as you can get using modern Technic pieces without some bulky over-engineered steering assembly.
My last thought on this takes us back to my earlier comment, "The majority of Lego racks are not beveled." Another option, and perhaps the easiest and most compact, would be to retro-fit the older rack pieces parts# 2790, 2791, 2792 into your build. These parts were pretty much made for this type of thing. Here's a couple pictures from set# 8832 for reference.