You've got a few options, though honestly none of them are going to fit your ideal scenario.
1) As Kevin Lee suggested, just do 30 seconds sprint, let it slow down and do 30 seconds walking. You're still doing intervals. If you're worried about the time that the treadmill is spending changing speed, then shorten your walking period to take that into account.
2) Get off the treadmill and go sprint outside (up a hill is better). No, you can't keep an accurate record of the speed, but it probably doesn't matter that much as long as you're still going all out during your sprinting periods. This has the added benefit of being self limiting, so as you get more tired, you'll naturally sprint slower, instead of stumbling on the treadmill and ending up embedded in the vending machine opposite.
Also, unless you're using the treadmill on an incline, sprinting outside recruits the hamstrings a lot more, so is a much more complete exercise.
3) Use the hop on / hop off method. Get the treadmill up to your sprint speed, sprint for 30 seconds, then, using the sides / arms / grips / non-moving-parts-within-reach bits of the treadmill, hop off so you're standing with your feet either side of the moving belt. After your rest period, (slowly!) lower yourself onto the moving belt and sprint again.
I've seen a few people use this method, and it seems to be a reasonably good option. Obviously, you're not getting your walking periods in, you're only getting the sprinting parts, but they're arguably the most important bits of HIIT.
4) Use another machine that makes it easier to adjust the speed, i.e. exercise bike or rower (as suggested in the comments). If you want the most bang for your buck and a challenge, do tabata front squats. If you can still walk afterwards, you're not going hard enough :)