Yes, 任せているために is the modern plain version, whereas 任せているがために is its literary (and perhaps emphatic) equivalent. This が is an archaic possessive/noun-linking particle that is still in use in a few fixed constructions including this one. ~んがために is a literary version that also has an archaic volitional auxiliary む/ん.
Modern ために means both "because" and "in order to", but I think plain-form + がために
tends to mean the former because it lacks む/ん. For example, 車を買いたいがために貯金する sounds fine, but 車を買うがために貯金する and your second example sound a little unnatural to me, if not wrong. 車を買わんがために貯金する and 身を守らんがために sound much more natural (although stilted).
|
ために |
がために |
む + がために |
Godan |
買うために in order to buy because someone buys |
買うがために (usu.) because someone buys |
買わんがために in order to buy |
Ichidan |
見るために |
見るがために |
見んがために |
Suru |
するために |
するがために |
せんがために |
Past |
したために |
したがために |
N/A |
Na-adj |
有名であるために 有名なために |
有名であるがために 有名がために (rare) |
N/A |
I-adj |
美しいために |
美しいがために |
N/A |
For details, please see the following questions: