so far that you are not joining after graduation, MBA or very few years of working experience, you would be considered an experienced hire by almost all the firms. As a consequence, your profile would be interesting mostly for the industries you worked before joining.
It could make sense thus to actually emphasize your IT knowledge, in particular for strategy related projects; as Thales mentioned, trying to hide them would mean trying to be considered as generalist, which would be pretty difficult given you have already experience and completed an MBA.
It is not clear which kind of IT projects you did - the closer to strategy, the easier the transition would be. In any case, the definitely best thing you could do to increase your chances would be to network inside the firm, ideally with alumni of your current company who joined the other firm. In this way you could both receive a referral and understand which part of your experience would be more valuable for that company.
As for how referrals work, you can find some more information at the second post I wrote at the following link:
Hope this helps,