No, you can't. Not accurately. The best you will do with this method is approximate the linear interpolation. You're arguing in a circle, see below. Here is your circularity. You need sigma to calc strike, but sigma (vol) is what you are looking for in the first place, Well if it actually worked you could rearrange the equation above to get sigma in terms of d1 and strike. The code you posted, using pnorm and qnorm instead of the more usual N, Phi, etc.. suggests that you program in R. If so, and you want to see the complexity of a rational function fit without the Pade trick, type the following in R console: require(pracma) rationalfit
If you want to see how delta changes over time, use a pricing model and advance it one day at a time, keeping all other variables constant. Time affects IV, delta and price but if you fix delta in the formula, you're monkeying around with the entire premise and then you are calculating how IV and price will change if delta doesn't change.
When I read your posts I realize how little I know about options beyond my retail trading. Thanks for your ongoing contributions here.