I do not consider neoliberalism to be a modern Marxist invention, though I can't claim to know about its history, and of course hitsory is extremely important to reveal a movement's origin and aims. My reasoning is from the idea that neoliberalism supports private property and what Marxists see as a class society. It does not aim for the abolition of these classes, but rather its stated goal is to acheive development within the capitalist system.
In this way, neoliberalism is identical to social democracy in its overall aim - it works within a class society to try and bring better conditions, though people frequently criticise neoliberalism as being uncaring of the poor, the Marxist would say a similar thing about social democracy.
For a read by a thinker inspired by Marx, I've heard good things about David Harvey's A Brief History of Neoliberalism. I have not read it, so I don't know if I should recommend it, but since you mentioned modern Marxists, and he is one, it may be of some use to you.
[0] https://newleftreview.org/II/49/alain-badiou-the-communist-h...