It seems like you have the years of experience and salary to match most Manager/Senior Manager specs.
If you feel like your sales track record is a strong differentiator, try to understand what sales targets are associated with the role and adjust your positioning on that basis. Those will vary between companies but not hugely.
On one hand size of billing won't be as relevant as your subject matter expertise (which you should have in spades at that level.) On the other, what it takes to win (and deliver) a 100k piece of work will be quite different in scope, effort, structure etc. from a deal 10-30 times larger. You seem to have a very good self-awareness (i mean this in the least condescending manner possible) on that front so good on you.
My advise would be to aim for both and seek to negotiate up when possible. While it's not gonna be easy it will achieve the following:
a) you will have a larger target (there are only 5 Big ones)
b) you improve your initial chances. You clearly exceed the spec for SC, so if you get invited you have the chance to position yourself up. Worst thing that can happen is you get turned down because they don't have space for someone at your level, and you have poetic license to bug them about future opportunities.
And yes, what a07 said is spot on.