No, because two of the same do not stack.
Even the caveat in Xanathar's is there just to save people from overhinking thigs, but is irrelevant. Both features say the same text:
Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it.
Or the other feat:
You gain proficiency in the Investigation skill. If you are already proficient in the skill, you add double your proficiency bonus to checks you make with it.
Even the rogue feature:
At 1st level, choose two of your skill proficiencies, or one of your skill proficiencies and your proficiency with thieves’ tools. Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.
You can pick them, but all of them do the same thing. They set the value added to the skill check from proficiency to double. You can pick and choose what doubling you want to use, but in the end it is just that. double.
It is the same thing as trying to get five +2 longswords to get a +10 to hit and to damage. You use one or the other, they don't stack.
Also analogous is the AC from wearing armor or other effects. Like the barbarian. Their base AC is either 10+CON or the AC value of armor. Do not stack.