What type of white are you using?

Try to glaze your midtones with a transparent dark mixture to assist the gradient from midtone to shadows as needed, you don’t have to nail the transition in an opaque fashion.

Edit: Or you could make a value scale to the side and compare your mixture to your scale as needed to ensure you have it close when painting opaquely.

My problem is white paint.
When I block in shadows and the rich darks everything looks good, I have a nice rich gradient of darker values and I’m now going to transition into the lighter darks and dark lights (sorry don’t know how to say this better.) As soon as I mix in even a little bit of white paint the whole thing goes amiss – there is no cohesion or flow between my rich darker values and the midtones that have white in them – even if they are close in value. I’ve tried mixing haltones without white but I can’t get the values light enough.

Zinc White can work fine for color gradient mixing. Titanium can cause “chalkiness” problem for many artists. Art creation is a combat with painting materials! But some specific pigments are effective to mix with Titanium White “chalk bomb”. For example, Phthalo blue; Phthalo green; Opaque red oxide PR101; Violet oxide PR101; Chromium Oxide green PG17; Diarylide Yellow PY83 have perfect mixing properties for gradients with Titanium White.

Titanium Buff has a high tinting strength also?

I saw this in my local art store yesterday, but haven’t found good info about this pigment…

Is the same that “Unbleached Titanium” from Williamsburg?

Titanium Buff can make mud with blue, violet, green or rose color. I found it completely not useful for me. I like superior White like Original Permalba White! I can add dirt into Titanium White by hand! I like chromatic white, but I prefer to use many different earth colors for that purpose.
In the other hand, some of low tinting and highly filled “mixing whites” can be nice to mix, but this mixing white can darken and became more transparent when dries. The real, good Titanium White is superior color. Also, those “mixing whites” have not documented paint formulation. Zinc White is better for mixing and sometimes irreplaceable for me, but people worrying about cracks in this paint. Finally, a little more experience in paint mixing will help to work with high quality artistic Titanium White!

When I block in shadows and the rich darks everything looks good, I have a nice rich gradient of darker values and I’m now going to transition into the lighter darks and dark lights (sorry don’t know how to say this better.) As soon as I mix in even a little bit of white paint the whole thing goes amiss – there is no cohesion or flow between my rich darker values and the midtones that have white in them – even if they are close in value. I’ve tried mixing haltones without white but I can’t get the values light enough.

Are you mixing white into your dark colours to make them lighter?

I keep white paint away from all the dark areas, if thats what you mean – I just start adding white into the midtones.

A common mistake is to add white to a colour to try to make a lighter version, but white, any white, will generally lower chroma.
(The exception is when white is added to very dark, very chromatic transparent colours like the phthalos, which will increase in chroma to a point before becoming less chromatic again.)
So I was wondering if this is what was happening to you.
As Don suggested, it may be that you’re just not mixing the right colour rather than white being the culprit.
This seems like good advice to me.

If the white paint is reducing the color intensity, then you need to start with more intense color, use less white, or find a more intense light color to put into the mix.

As you come from watercolour, it may be that you just don’t like the opaqueness you’re getting.
If that’s the case, you could use transparent oils in a similar way to watercolour and not use white at all.
You can’t do washes in the same way because too much solvent destroys the paint film, but you can still paint very thin transparent films with good technique.
I’m not sure, but I don’t think that Maxfield Parrish used white unless blocking in an area if repainting something.
Anyway, it’s certainly possible not to use white.

Maybe if you posted a photo we could get a better idea of your problem.