There are various ways to hedge a portfolio and "better" is in the eyes of the beholder because there is always a trade off decision between cost, as well as the amount of protection and profit potential at various prices of the underlying - in this case, a composite of the DJIA and Ford prices.
There are several problems with your idea to hedge a portfolio with deep OTM Ford puts.
First and foremost is correlation risk. You are making the assumption that Ford will drop nearly 50% if the DJIA tanks 30%. That may come to pass but if not, your hedge will be worthless while you have lost $300k on your million dollar portfolio (Ford drops 30% to $8.23).
Option premium is non linear so buyers should purchase further expirations because the cost per day is less. In this case, it's irrelevant because your $8 puts are so far out-of-the-money. Despite that, consider one year LEAPs. The June 21, 2019 $8 put costs 16 cents so $20k buys 1,250 of them. Assuming that your prediction is correct and that Ford is $6 at expiration, that will net you $230k (while losing $300k on the DJIA). If probability amuses you, your put has a delta of .08 which means that the likelihood of expiring in the money is approximately 8%. If it existed, the June 21, 2019 $6 put would at best have a delta of .01. That's a 1% chance that you obtain $230k from your $8 put. How do those odds sound to you?
On a quid pro quo basis, if the DJIA fell 20% tomorrow (down $200k), and assuming that there was no expansion of implied volatility, your 1,250 June 21, 2019 $8 puts would be up $40k after a 20% drop in Ford. Does that look like a good hedge at that point in time?
The short answer? The use of deep OTM Ford puts as a hedge for the market is a lottery ticket with a lot if IFs.
If you have some ability to identify stocks/sectors with a beta greater than 1.00 that would be more likely to drop more than the DJIA then if you insist on the cross correlation hedging, set up a basket of long puts on 10 or so of these stocks. It's not etched in stone that it will work but it's better than putting all of your hedging eggs into one stock. In addition, if any of the 10 collapse in the interim because of their own stock specific issues, you'd cash those puts in and redeploy a portion of the gains elsewhere. To some extent, this basket might fund some of the hedging costs even without a market correction.
For my taste, I'd prefer hedging of a portfolio with its own options so that you know what the P&L will be at various prices (no cross correlation risk). In that vein, a low/no cost collar would be a possibility. You could construct it with whatever P&L limits deemed acceptable. For example, a 10% wide collar on the SPY (DIA doesn't offer 1 year options now) might cost about 3% but with a yield of 2%, it could cost as little as 1% per year. Assuming full cooperation of the underlying, 9% profit and 11% downside risk. Or if you prefer a wider P&L range, you could do a 15% or 20% wide collar. And if you are willing to accept a modest amount more of of risk, you could do an imbalanced collar for no cost or possibly a small credit. Lots of possibilities.
If going the collar route, I'd use expirations 4-6 months out. That way, if the underlying cooperated and rose toward the upper strike, you could roll it up and out, maintaining a similar R/R range while locking in some of the gains in your portfolio.