Another possible solution
The teak on our boat is over 35 years old and was in real rough shape (moss growing on it, splinters in skin, and just plain weathered). So I was ready to make replacement parts for all of teak but I didn’t have the time or money to do so, and I knew from past experiences that the 3 step process, more than likely the same 3 step process you’ve used, seemed like a waste of time especially for the amount of work and time spent into trying to make teak look good. I went to my local marina and asked them what they use or what they would suggest. The process they suggested is very similar to the three-step process used in the past but instead of oiling the teak you actually use a product known as Sikkens Cetol Marine translucent sealer (about $30 a quart). So I cleaned our teak, sanded it using 80 and 100 grit, used the brightener, and lastly put 4 coats of the Sikkens on, (it’s really important to read the instructions before applying). This is a time consuming project because you have to wait 24 hours before applying each additional new coat, but our teak looks great. Lastly this product is meant for marine applications and specifically mentions teak as a wood that can be sealed where many products are not meant for teak because of its oily nature. Sikkens does give a sealed look to the wood meaning that it gives a semi glossy look when done, but to me I’d rather have my teak sealed and looking good for many years to come rather than spending the same amount of time on the typical 3 step process and have it look good for, at worst a week and at best a season. So if you don’t like the grey weathered type of look (which I don’t but many do like that look) and don’t want to have to clean and oil your teak every season, I would suggest using this product. Good Luck,Curt