Irrespective of the nylonish link bushing(s) being gone (I've also got one on my current do list), if you can get it in any forward gear then you should be starting out in 1st before it upshifts to 2nd. I don’t believe the AW30 is any different from the AW7x in that regard. A fluid level check and likely needing a thorough trans flush should still be on your list.

Going back to my kickdown thought, in the FAQ you’ll note about being able to hear the pawl on the end of the cable faintly plunk against the bottom of the kickdown chamber when the adjuster nut is backed off sufficiently and you pluck the cable. If your trans is gunky enough to have such upshifting problems then you may not be able to hear that plunk easily, if at all. a) Be extra careful to count nut faces so you can restore kickdown to the original adjustment if needed, and b) Be extra thorough with your flushing.

BTW The genuine Volvo trans linkage bushings are well known to be of harder material and more difficult to install than aftermarket equivalents and consequently longer lived. After all the ones you've done, I’m sure you’re aware of the need soften and lubricate them as Spook mentioned.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now