Thumb position is an upright technique where in the upper registers of the neck (generally around the "12th fret"), you bring your left thumb onto the fingerboard and use that as your 1st finger. Generally in this position you would use thumb, index, middle, ring, and not use the pinky. What you're doing is totally different as you'd have to approach the neck from the other side because your strap is so low.
I really recommend you think again about having your bass so low. You say your right hand is straight which is comfortable, but your left hand must be at some horribly awkward angle. Other than looking cool (if you think it does), from an ergonomics standpoint you absolutely want your bass to ride higher. This will allow both wrists to remain at a healthy angle.
You may want to read :
http://www.adamnitti.com/bass_player_03.shtml
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Avoid sharp wrist angles
The importance of this can not be overestimated. Sharp wrist angles, combined with tension and fatigue, significantly contribute to bass players hand injuries, and these injuries can sometimes be irreversible. Although problems such as carpal tunnel syndrome, repetitive stress injury, and tendonitis are beyond the scope of this particular column, their prevention is aided by the avoidance of excessive stress on the wrists.
In general, you want to keep your bass at a height that allows a moderate wrist angle for both hands. You will find that if your bass hangs excessively low, a sharper angle is incurred by the wrist of the fretting hand. If you wear your bass excessively high, the wrist of your plucking hand will incur the sharper angle. Even if a player wears his/her bass somewhere in between, most end up struggling with wrist tension when they are playing in the lowest register of the bass, closest to the headstock."