I have another option. Didn't think about this until today.
Swords and Wizardry White Box is the perfect place to start. The book not only covers you with regards to the OGL, but allow you to utilize their text, under their own Open Gaming License, providing you follow a few simple requests stated in the license. You may take the entire text word for word, modify the sections that you desire, add new sections, reword whatever you want and then republish it as your own product.
There are many examples of commercial and non-commercial products that have done so. Some were very basic, such as this: https://www.drivethrurpg.com/product...dventure-Game? where the guy simply modified about 4 pages total (basically added his own house rules) and then republished. Both S&W whitebox and this text are free pdf's. You can check out easily what minor changes were made. Other's were very extensive modifications to make completely new games such as: https://www.drivethrurpg.com/product...ation-WhiteBox which is a commercial product and https://www.drivethrurpg.com/product...ords--Wizardry which is another commercial product that is an extensive modification of S&W.
I think this is the perfect solution for you. You can change whatever you want, but have the option of saying, ehh, I'm using the same initiative system as they are, why do I need to reword anything in that section, on to the new stuff I want to add. You also can use or not use the OGL, but it will be there in place by virtue of using S&W white box as your base text.
If anyone ever comes up to you and says, this looks suspiciously like xxxx from company yyyyy, you can pull out your copy of S&W white box and show them, this was my base text, not that other thing. It says here in their license that I could do these things.
Personally, I would like to see what creative things you can come up with. An orc is an orc is an orc. Dare you come up with some new beasties? Now that would be cool.