Screw Mullein - get some last year's Teasel. You'll have to be selective, though, because being this old, most stalks will have cracked. This doesn't mean Mullein won't work, because it does, I just don't particularly like it. Having said that, Mullein might be a good choice now because its stalk probably aged better. (If this doesn't make any sense, it's because I just woke up)
If you go with Teasel, the thicker the wall thickness, the better. Also, the rounder the stalk is at the business end, the better - some stalks are more oval in shape. If you can't find any intact pieces that are long enough, you can always splice a tip on some other stalk.
As far as length, my technique is dictated by a herniated disc, so I choose a drill that is from ground to navel in height (41-42") (It's good to use body measurements for things, because you always have it with you

)
You want a drill that is large enough in diameter to oscillate easily, but not so big that, a- the friction is spread over too large an area on the hearth, and b-your speed is adversely affected.
The following are
drill/hearth combinations that I have successfully used:
Teasel (Dipsacus syvestris)
Willow (Salix spp.), Cedar (Thuja occidentalis), Sumac (Rhus typhina), Cottonwood (Populus deltoides)
Burdock (Arctium lappa) [not recommended] on Willow.
Great Ragweed (Ambrosia trifida) on Willow, Sumac, Cedar.
Mullein (Verbascum thapsus) on Willow.
Sweet Clover (Melilotus - don't remember the species) on Willow, Cedar.
Sumac (spliced tip) on Willow.
Thistle (Cirsium vulgare) on Willow and Eastern Cottonwood.
Willow on Willow and Cottonwood.
Eastern White Cedar (T. occidentalis) [spliced tip] on Cedar.
Dogwood (Cornus - didn't note the species, though probably sericea) on Willow.
Eastern Cottonwood (P. deltoides) on Cottonwood and Cedar.
Jerusalem Artichoke (Helianthus tuberosus) [probably my all-time favourite] on Willow and Cedar.
Canada Goldenrod (Solidago canadensis) [stalks large enough in diameter not too common] on Willow.
Basswood (Tilia americana) on Basswood.
Cattail (Typha latifolia) on Cottonwood.
In case you're wondering, Tf, no, my memory isn't that good. I kept a log of my first 500 hand drill coals - materials used, weather conditions, any particular problems, state of sobriety

, - those kinds of things so I could go back for reference purposes (such as this post). This, I recommend to anyone for both bow drill and hand drill. Notes last longer than memory.
More recently, Basswood is my hearth of choice and Teasel for a drill, in part, because of availability, although Jerusalem Artichoke would be my first choice.
Since you live in Texas, a list that might be more appropriate for you was compiled by a late brother, Storm (AKA Firestorm). If you want the list, I'll look for a link.
Whew, now I'm almost awake.
Doc