You can ready a concentration spell

When you ready a spell you completely cast it and hold the energy but none of the effects of the spell happen until it is released.

If your concentration is broken, the spell dissipates without taking effect.

The spell-specific concentration aspect doesn't take effect until its release just like the duration and other effects/attributes don't start taking effect or counting before it is released. The spell-specific concentration starts when the duration of a spell starts. And the duration of a spell starts when the spell takes effect (so upon release in this case).¹

Thus, since there is only one source of concentration active when holding a spell, there is no conflict and the Ready action proceeds as normal.

Also, regardless of the above logic, if Ready was meant to exclude concentration spells it would have come out and said so instead of relying of really minute logical inconsistencies to do so.

The Crawford ruling doesn't change anything here

Regarding the Crawford Tweet looking at the full sentence reveals its context and why it does not affect this case:

A concentration spell ends the instant you start casting another concentration spell, and a spell takes effect when its casting ends. If you cast invisibility in succession, you're visible during the 1-action casting time—effectively for a split second or so.

The ruling doesn't matter here because there is only one spell and one source of concentration happening at a time when you ready a concentration spell.

^{1 - If duration was counting during the held part of readying then it would be impossible to Ready instantaneous spells because their duration would have expired the instant after you started holding their energy. And the book explicitly gives the example of readying magic missile as a valid ready action. Thanks @Gandalfmeansme for this suggestion.}

If you don't spend your action casting the spell, you have stopped casting the spell

There are only a couple of possibilities for what could happen if you start casting a spell with a long casting time and then don't use your action to continue casting it:

1. The casting continues uninterrupted, and this round counts towards the casting time.
2. The casting is paused, so this round doesn't count towards the casting time, but you can resume casting next round as long as you maintain concentration.
3. The casting is cancelled, and you would have to start over from the beginning if you still want to cast it.

I can't think of any other reasonable interpretations of the rule besides these 3.

Option 1 is directly and unambiguously at odds with the rules, which say that "you must spend your action each turn casting the spell". So we can eliminate it right away.

Option 2 seems plausible, but there are a lot of problems you need to address if you use this interpretation. For example, how many rounds in a row can you "pause" the casting before the spell is lost? Could you pause casting a spell 1 round before you finish, and then wait indefinitely for the opportune time to complete it, thereby allowing you to set a trap with a spell that normally has a prohibitively long casting time? In short, Option 2 implies a whole new set of possible mechanics relating to "paused spellcasting" and its interactions with other mechanics, none of which are addressed at all in the rules. That makes it very unlikely that this is the intended reading.

So, having eliminated those two options, the only reasonable interpretation left is Option 3: the spell's casting is cancelled. This is certainly the most literal reading of the rule: if you spend your action each turn casting the spell, you cast the spell; if you don't spend your action each turn casting the spell, you don't cast the spell. The rules don't say that the spell fails if you don't use your action to cast the spell, because they don't need to. The spell doesn't fail: you simply don't cast it because you stopped casting it. The requirement to maintain concentration through the full casting time is an additional requirement to cast the spell and is unrelated to the requirement to spend your action each turn casting it.

(I agree that this logic gives an absurd result when combined with the rule that a surprised creature cannot take an action on the first turn of combat, but I would argue that the fault lies with the surprise rules, not the spellcasting rules.)