I have my z offset set to the top left corner of my stock. I jog my machine so that the tip of Tool 1 is touching the zero point. I hit Zero X, Zero, Y, Zero Z on the DRO. My tool table values in the length column are
T1 = 0
T2 = -0.2758
T3 = 0.1304

Then I run the following g-code:
G90 G94 G91.1 G40 G49 G17
G20
M5
Z3
T3 M6
G54
M8
G0 X13 Y-24
G43 Z1.3783 H3
Z0.9846
G98 G81 X13 Y-24 Z0. R0.9453 F14.2
Y-23
G80
M5
M9
T2 M6
G55
M8
G0 X13 Y-24
G43 Z1.3783 H2
Z0.9846
G81 X13 Y-24 Z0. R0.9453 F17.2
Y-23
G80
G0 Z1.3878
G90
Z3
G17
M9
M30
When T3 is loaded it doesn't go deep enough, short by about 1/8",
T2 trys to go about an inch to deep

I though the line
G43 Z1.3783 H3Would move the machine down an additional 0.1304" when drilling with tool 3, and move down -0.2758 less with tool 2. Why is it going to these seemingly random depths.

What is going on?, what's it supposed to be doing?
 

Try removing the Z value after G43.
This is part of some code I've used on my machine without any problems

(Andys Mincer Plate.tap)
N5 G90 G20 G54 G28 G40 G80
(Setup 1)
(Work Zero)
(Spot Drill 2mm Cutouts)
N10 M09
N15 M05
N20 G53 G00 Z-0.1250 (Tool Change Position)
N25 G54
N30 T01 M06 (6mm Spot Drill)
N35 G43 H01
N40 S5000 M03
N45 G00 X-0.1181 Y1.0465
N50 G00 Z0.0400
N55 G81 X-0.1181 Y1.0465 Z-0.0150 R0.0400 F4.
N60 X0.1181 Y1.0465
N65 X0.1181 Y-1.0465
N70 X-0.1181 Y-1.0465
N75 G80
N80 G00 Z0.0400
(Spot Drill 1.5mm Holes)
N85  X-0.6264 Y0.6264
N90 G00 Z0.0400
N95 G81 X-0.6264 Y0.6264 Z-0.0150 R0.0400 F4.
N100 X-0.4921 Y0.7365
N105 X-0.3390 Y0.8184
N110 X-0.1728 Y0.8688
N115 X0.0000 Y0.8858
N120 X0.1729 Y0.8688

Just had a quick read of the manual and if you want to retain the Z move, then add it after the H value,  G43 H3 Z1.3783

Hmmmm, isn't your G81 line drilling to Z0? So with the tool length offset applied, .1304, wouldn't it drill to PLUS .1304, "short by about 1/8"?

Don't know why T2 would be going about an inch too deep, it should be .2758 too deep assuming your drilling to "Z0" as your G81 lines indicate.

What's generating your gcode, or is it hand written?

And, I don't think the G43 line matters what order the G43, the H3, or a Z move are in.

And, I don't think the G43 line matters what order the G43, the H3, or a Z move are in.
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Whilst I agree in principle with this statement, I find that if there is a problem, then it's best to follow the format shown in the systems manual, to remove one possible problem source.

As you correctly point out, because the code calls for a drill depth of Z0, it does appear that the OP's tool lengths are incorrect.