The idea is to tune the antennas so that using a tuner isn't ~very~ necessary. That will usually have better results than otherwise. Then, if using that tuner will make the input impedance more acceptable to the transmitter, good.
Since you have three antennas in one, and since each will affect the others, finding the right lengths for each is a make changes and check to see if other changes are necessary type of thingy. Count on there being a lot of those changes and checking thingys! That's about as normal as it gets no matter if you're talking about one antenna or a bunch of them. The way you're going about it, finding out what the SWR is at various frequencies, is a very good way of figuring out what has to be done to make things better. Other wise, it's just a shot in the dark, you know?
Somewhere in all that checking and adjusting you will think this is a bunch'a @#$% and just use the tuner to make things 'better'. The quicker you reach that point, the less effective your antenna system is going to be. So, stick to it, don't 'quit' too soon. There's also diminishing returns the 'better' things get. The first change or two can make a big difference, but after that the differences get smaller. You have to decide when it isn't worth more effort.
About that 'grounding'. Ground rods are much less effective than ground radials. Those rods are easier to do than the radials but they just don't end up doing as much. Sorry 'bout that, but it's a fact. If you really want to improve things by adding to the antenna's counterpoise, their 'other halfs', then do the radials instead. (I hate radials, mainly cuz they are a lot of work. Oh well.)
Good luck and have fun.
- 'Doc