I've had quite a few grain-free (well. grain-, dairy-, sugar-free) phases since age 16, though I am not - thankfully - totally gluten intolerant, I can normally eat spelt and oats etc quite happily. But give me some kind of infection or other (or an allergic reaction to sth else, worst was having those tooth-fillings with mercury in, which I'm allergic to) and my body can't cope anymore. And if I'm trying to lose weight, grains are out too.
So I've tried a few ways, from lots of replacement-dishes to a complete diet change, and I have to say the complete change works best and fastest for me for the initial clean-out (again, with exception of the cranky factor, but that could be due to the fact that initially it's quite hard to get the same amount of calories down in the form of lentils, so I might have been hungry) - I guess it was psychologically the easiest because I wasn't anywhere remotely near the things I was no longer allowed to eat, so had no comparison, and totally different expectations of what would be on my plate. Omelett with peas tomatoes and scallions for breakfast was far enough from cereal or toast for me, buckwheat porridge wasn't ... slippery slope, cheesecake ensues... but that's me, and it took me a while and a lot of being honest with myself to figure out that no, I would NOT be able to resist next time either

Then, once a week regularly and whenever there was something to celebrate, I'll indulge in something like an almond flour chocolate cake, buckwheat pancakes, coconut cupcakes etc ... so it's not a can't have, but will have later.
This got me over the first few weeks, and after that, new habits in place, blood-sugar stable, the slippery slope is no longer a problem.
What kills it for me usually is spending weeks or months away without the time to cook for myself, or my own kitchen, or enough animal protein ... eventually it always ends in cheesecake

. So right now I am starting over again. I love the lightness that is spreading in my body already and the no longer being bloated ... and I've started waking up earlier and with more energy only 2 weeks in. If it really is the grains that are giving you trouble, you will LOVE the changes and probably feel them quite quickly.
P.S. THE fastest way I'v tried would be to fast/colon cleanse, but I wouldn't do that unless you can take a week off - it's rather radical detox and I found it made me not just cranky but very 'thin skinned' - not a good idea while working.