For stage lighting, I prefer to use prime lenses... which can offer larger aperture than most zooms, plus are smaller, lighter and often less expensive. Check out Canon EF 24mm f/2.8 IS USM, EF 28mm f/2.8 IS USM, EF 28mm f/1.8 USM, EF 35mm f/2 IS USM, EF 50mm f/1.4 USM, and EF 85mm f/1.8 USM, in particular. The EF 135mm f/2L USM is also great, though it's a lot more expensive.

The Tamron "Di" lenses are full frame capable ("Di II" are crop only), which will necessarily make it bigger and heavier than a crop-only lens such as the Canon EF-S 17-55mm f/2.8 IS USM.
Most zooms are f/2.8 at best. It can be a big help to have one or two more stops, such as many of the primes provide. (Yes, a couple of the primes mentioned above are f/2.8, too... but they're wide angle that don't need as fast shutter speeds and tend to be a bit smaller, lighter and less expensive than zooms covering the same focal lengths. There are some faster wide angle avail., but they tend to be less sharp in the corners and give up the advantage of size/weight/cost, plus in some of the wider have a protruding, convex front element that precludes using standard filters on them.)

All that said, for portraiture I do like a 24-70mm on an APS-C crop camera (like your 70D). It's a nice range of focal lengths. I switch to a zoom when shooting kids or pets, for example... Less predictable subjects where the zoom might be necessary. I use Canon 24-70mm f/2.8 (no stabilization, which doesn't bother me on shorter focal lengths like this.... though I do LOVE stabilization on telephotos and it's one of the key reasons I switched to Canon in 2001.)

I hear good things about Tamron's most recent 70-200mm f/2.8.... But I use Canon's, which are among the best made by anyone (For decades Canon has used fluorite in many of their telephotos, which makes for less chromatic aberration and sharper images. In fact, within last year or two, Nikon has also redesigned many of the telephotos to use FL. No one else, Tamron included, uses it due to the cost and difficulty working with it.)

Some of the above Canon lenses have IS, which I'm sure in most cases is AT LEAST as good as Tamron VC (after all, Canon invented stabilized lenses for SLRs and DSLRs, so has been making them for many years longer than Tamron and everyone else who have merely followed Canon's lead). Canon USM focus drive also is their fastest and highest performance (Tamron USD is essentially a copy of that, likely with similar performance... which their 24-70mm has, but I don't think your 16-300mm does.)

A Tamron I use... their SP 60mm f/2 Macro/Portrait (crop only) is great! But it's not stabilized and it has slower focus drive (probably micro motor, I don't think they specify). It's fine for macro and portraiture... but not for any sort of action shooting. Too slow to acquire focus for fast shooting situations and not able to reliably track anything moving faster than a relatively slow walk. I've also got an older version of Tamron's 90mm macro now... and I've used a variety of their other manual focus lenses in the past. They're "SP" line, in particular, has been among my favorites.... They've recently introduced several impressive looking primes, too (haven't used them and don't know how they compare).

To tell you the truth I don't use, don't like and never will own a "do everything" zoom like that 16-300mm. The reason I bought a DSLR/SLR was to be able to interchange lenses. I see no reason to compromise in many ways (various image quality factors, focus performance, really small max apertures, limited close focusing ability & possibly more) just to be "convenienced" by never having to change my lens! If that were my goal, I would have bought a non-interchangeable "point n shoot" camera, rather than turning my DSLR into one!

Whatever you decide to do, I think you will find the lens upgrades very worthwhile (lenses very often make a lot more difference in the quality of your end results... than the camera they're used upon).

EDIT: I hate to see folks have motion blur problems because they are afraid to use higher ISOs. I suggest you experiment with higher ISOs.... Might be surprised what you can do. Following was shot with 7D Mark II at ISO 16000 (yes, sixteen thousand, not sixteen hundred), which has similar sensor to your 70D....



You can see some noise in the enlarged detail on the right (which is a lot larger than I'd ever print the image). But I think it's pretty well controlled. This high ISO test mage was shot RAW with care to avoid underexposure (boosting exposure in post-processing ALWAYS amplifies noise). It was then converted to JPEG through Lightroom only using default noise reduction settings. Normally with high ISO images I do additional work using Photoshop with a Noiseware plug-in. But this was a "worst case" test. And I think the camera passed pretty well! You may not be able to use quite as high ISO with your slightly older camera... but you should test how far you can push it. I kept to no higher than ISO 6400 with my older 7Ds... and ISO 3200 with my 50Ds before that.

In addition, stage lighting is often a lot brighter than folks realize. It's often concentrated spot lighting, but sometimes nearly as bright as daylight.

First post here but would love some help. I am definitely an amateur and shoot with a Canon 70D and love it for what I do. I primarily shoot landscapes, nature but also lots of pics of my son and his band. My primary lens is a Tamron 16-300 f3.5-6.3. I am looking to upgrade to a faster lens primarily for the concert pics as it tends to be more challenging lighting obviously. I do like the Tamron line especially with the Vibration Control and am considering the 24-70 f2.8 Di VC G2 SP. Most of the shots I take are closer to the stage so don’t necessarily need the longer focal length. Although also considered upgrading to the 70-200 f2.8. Would love to hear your thoughts and anything else I should consider.

Thanks in advance.

If you mean the IS USM version, its my personal favorite lens. Its on my camera more than all my other lenses put together. It's such an efficient light gatherer that in DXOMark tests it has a tStop of 2. TStops are a measure of light transmission and in the best cases the tStop will equal the widest aperture. Most lenses, even the best primes, have tStop values that don't match the widest aperture. Most f/1.8 prime lenses have a tStop of 2.1 or 2.2 or more, which means the Canon EF 35mm f/2 IS USM actual lets in more light then some faster lenses. a perfect example is the Tamron SP 35mm F1.8 Di VC lens which has a tStop of close to 2.5, a whole stop of light less than its maximum aperture would suggest.