Regarding your S&P Volatility analysis i like the idea to use it as a psychological support in times of uncertainty, but i guess i would never use S&P related indicators for BTC trading. The reason is simple, S&P cycles are much longer than BTC cycles and i would not mix them.
I agree, S&P volatility is not very helpful for trading as shown in my backtest. It outperforms buy and hold, but underperforms cycle valuation trading.
However I will add the volatility indicator to give me a rule based confirmation that the top or the bottom is in:

What I like about my bottom / top confirmation indicator:
- rule based
- no wrong signals up to now
- top confirmation is quite close to the real top
- bottom confirmation is still reasonable close to the bottom as a model maintenance trigger
- very interesting is that during the double tops 2013 and 2022 our indicator only shows us the 2nd top
What I dislike about my bottom / top confirmation indicator:
- The trigger is not useful for trading since the Bitcoin price has moved quite a bit when my indicator calls the top or bottom.

Regarding BTC we had some full cycles since 2010 and a lot of data Points relating to all cycle phases.
Regarding S&P we only have one big bull market since 2010 only interupted by some "minor" corrections.
The problem is not the lack of S&P-volatility signals for Bitcoin, we had more than 10 signals since 2015, ...

... the problem might be a possible change in the relationship between S&P volatility and Bitcoin during a long term S&P bear market. One example for a change in relationship would be the gold price. During the bond bull market gold moved inverse to real interest rates, but in the bond bear market during last few years gold decoupled from real interest rates. So relationships can change.
I would guess a liquidity or a risk event pushing the S&P volatility above average would definitely be bad for Bitcoin price in the short run. Especially since Bitcoin and legacy financial markets are connected via. ETFs and Futures.
The question for me is: Can we improve the cycle based entry points by using DCA as a money management tool (not as an indicator)?
Using time based DCA: Is it better to buy @ Trend price -40% / ln(-0.5) all at once or starting the saving plan for X month from than.

Is it better to buy @ Trend price -40% (= trend*e^-0.5) all at once. Starting the saving plan for X month from than yields you an underperformance for all X. For X = 12 you get an underperformance of e⁻0.4 = 33%
Using price based DCA: Is it better to buy @ Trend price -40% / ln(-0.5) all at once or split basket to buy @ -0.5, -0.6, -0.7, -0.8, -0.9 and -1.0 (and eventually miss the dip with some orders an have some FIAT left)?
Missing the dip and being partly invested in cash will yield you a significant underperformance over a whole cycle. We could reduce the underperformance by canceling the -1.0 after a certain time and placing a market order at -0.2 instead. On average you will loose with the -1.0 bet. Not only are you more likely to go from -0.5 to 0.0 than to -1.0, but additionally you have a positive trend.
Nevertheless I'm interested in this question as well to place the orders around a peak and a bottom. Not so much in order to get further outperformance, but form an operational stand point to not overburden my bank accounts with inflows triggering AML procedures in the bank. I can prove all my buys and all taxes are paid. However it is still a hassle I would like to avoid. Also some banks might dislike Bitcoin, despite buying Bitcoin is legal.
As Bitcoin prices increase, it is possible I can only sell 3% of my Bitcoin peer to peer. A centralized exchange CEX would make additional 10% sales possible. If I sell at the best possible moment, I could only sell 3% (incl. CEX 13%) of my holdings. Spreading it out over 4 months would make it possible trade 12% (incl. CEX 22%).