Interesting question. I'm not an expert, but I would think that the mechanical amplification process ends with the ossicles, and that the process that follows is the tranformation of energy from one medium to another (solid to liquid). I would think that the surface area of the oval window does have an effect on the energy transfer, but that it wouldn't make sense to classify it as part of the amplification process.

I`m not sure, but, It seems that the surface ratio between the round and oval windows can play a little role in stimulating the inner ear through the pressure deference, However this effect can be very small in the intact middle ear and get importance in cases of ossicular interruption or near-total tympanic membrane perforations..

"... Sound conducted down the ear canal sets the tympanicmembrane into motion, which condenses and rarifies the air within the closed middle ear airspace, creating a sound pressure, PME . This middle ear sound pressure stimulates the oval andround windows. Since for much of the frequency range of interest, the dimensions of the middleear spaces are much smaller than the wavelength of sound, the middle ear sound pressures justoutside the oval and round windows will be very similar to the pressure within the middle ear: PME=Pow=PRW' However, because of small non-uniformities in the cavity shape, Pow and PRW are not exactly equal and the difference, 6P = Pow - PRW' is non-zero but small. Bekesy (1947, 1960) and Voss et ai. (2007, see Fig. 3.10) measured the acoustically coupled Pow and PRW produced by an ear canal sound pressure and found the window-pressure difference (6P) to be 30-50 dB smaller in magnitude than the ear canal sound pressure. The small size of the acoustically coupled window-pressure difference relative to the ear canal stimulus points out that acoustic coupling is not an efficient method of stimulating the inner ear, although in cases of ossicular interruption or near-total tympanic membrane perforations the acoustically coupled 6P can act as the primary stimulus to the inner ear (Peake et aI., 1992; Merchant et ai., 1997; Voss et ai., 2007). "

(2010-01-14). Fuchs, P. (Ed.), Oxford Handbook of Auditory Science: The Ear. : Oxford University Press,. Retrieved 3 Aug. 2018, from http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199233397.001.0001/oxfordhb-9780199233397.

I think it may have some contribution, but there are lots of things that affect amplification. This is why we have to do a Real Ear Measurement for fitting a hearing aid.