I notice that all three links that you provide are the same white paper from the Republican Cato Institute which advocates for an education tax credit for preschool and K4 education. This white paper is not a research paper but simply an opinion piece.

The Institute still supports preschool education but opposes using public funds to fund it and instead advocates using tax credits to fund preschool education. Needy kids do not benefit from tax credits unless it's a refundable tax credit. And there's no difference between a refundable tax credit and a govt subsidy.

The white paper criticises normal researcher interaction with the families in their study for both control and test groups. Both groups have equal attention. The only difference is in the preschool experience. These is how research is done.

Here's a direct quote from the Cato Institute paper...

"...Credit aims to sustain any potential preschool benefits and establish a solid foundation for future success."