Seems like the only real way to play both Suits and Death House. Maybe get in a couple of the 4-1 missions- still level one, and get to enjoy some Suits of the Mists(and get sent to Barovia from Toril)... come upon Death House in Barovia, and then move on to 4-2 or CoS hardcover?
You could certainly do this if your players weren't terribly interested in running all 5 of the Suits missions (though they are interrelated, so it makes sense for the party to do all 5 if possible); having them head into the Mists early to encounter the Death House would be do-able. As an added bonus, if the party was already level 2 when entering the House, you as DM have less of an incentive to allow a long rest to be successful until the end of the module.
The characters could even transition back and forth between season 4 AL missions and the CoS hard-cover, though as noted, if they level out of the tier 1 story before completing it, they'll miss some story info. Likewise, since each chapter in CoS has a recommended level, characters who bounce back and forth may not get to encounter all of the hard-cover adventure.
The recommendation is to do one or the other -- pick CoS or season 4 AL adventures -- but if you're willing to do the work and your players are OK with possibly missing some content, you could certainly make it work for them to do both with the same group of characters.
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Pauper