OK, I'm a guy who's been known to put on a suit and play standards for the guy eating the pork chop. I've done quite a lot of it in the last couple of years.
I hear some post-modern cynical irony in your question, Peter. As in "I know I won't be considered the next Christian McBride, and I know standards have been done past death and are banned from the planet Cool, but silly me I'm gonna give it a shot anyway. Anyone have some advice for me in this pointless, low-brow commercial endeavor?"
Here's the advice: adjust your attitude! Pork Chop Boy may not be the audience you had in mind but forget about him, if you can. He may not show it but he's very easy to please and he'll help pay for your jazz education. What you need to do is try and connect with "Body and Soul", or "Stardust" or "My Funny Valentine" or whatever hoary done-to-death standard you're playing. There's a reason it's a standard: it's a thing of beauty! Savour them. The Cool Police aren't looking.
For jazz, concentrate on getting a strong rhythm pulse as soon as you can. The walking and the soloing can be developed over time -- start simple ande keep listening, keep imagining and keep trying to hit the mark. There's a hardly a better, safer way to log performance time than in the restaurant while Pork Chop Boy is clattering his cutlery all over the place.