Based on what I have seen, it appears that to a considerable extent, reverse is true. Some of the Rajput clans originated from Maharashtra/Karnataka region with absolute certainty. Some of the others are, to the best of my knowledge, branches of clans that originated from Maharashtra/Karnataka.
Rathore are same as Rashtrakuta. Solanki are same as Chalukya. I am quite certain that the Paramaras are a brach of Rathores, based on early Paramara copper-plates.
Consider these major Rajput clans:
Rathor=Rashtrakuta: of Jodhpur, Bikaner etc. 24 branches.
Gahadaval: of Kannauj. Regarded to be a branch of Rathors.
Bundelas: of Orchha, Datia etc. Regarded to be a branch of Gahadvals
Chandellas: of Khajuraho/Mahoba. Some obscure connection with Gahadval.
Paramara: Of Dhar/Abu. 24 branches.
Solanki=Chalukya: of Anahilavad. 16 branches.
Baghela: of Rewa. A branch of Solanki.
Silar: Shilahar of Kolhapur.
Some Rajputs do not appear to have originated fromMaharashta/Karnataka: Gahlot, Tomar, Kachhvaha, Chauhan, Parihar,Bhati.
We should note that emergence of Rajputs coincides with expansion of Rashtrakutas and Chalukyas into western/northern India.
It is also interesting to note that around the same time lineages of Jain Bharratakas (Sarasvati-Gachchha-Balatkara-Gana as well as Pustaka-gachchha-Desiya-Gana) appeared in North India. Also, theSenas appeared in Bengal after having moved from Karnataka. Rajatarangini of Kalhana mentions about adaptation of Karnataka customs in Kashmir!