I do think the designer was a bit optimistic.
The engine in the FDB-1 was rated at 700hp/2250rpm for take-off and 650hp/2200rpm at 7500ft max continuous. No military rating but with only 50rpm or so margin it doesn't seem like much. The 261mph speed was recorded thousands of feet higher. much higher than RAM effect would account for.
The proposed R-1535 SB4-G was rated at 825hp/2625rpm for take-off and 825hp/2625rpm at 7200ft military and 750hp/2550rpm Max Con at 9500ft which is certainly a healthy boost.
However the cube root law calls for about a 46% increase in power to go from 260 to 290mph, let alone 300 mph. The account makes no mention of the altitude at which 300mph was to be achieved.
If the original power plant was so worn out as to significantly affect performance the plane probably should not have been flying at all. This was neither wartime or an airfield in a war zone far from factory support.
The part about the R-1830 engines also seems a bit iffy, It is said that it was to be the same engine used in the XF4F-3 which was the two stage engine. We can assume the proposed 365mph was to be at an altitude that favored the two stage engine but we have to believe that the FDB-1 would have much less drag than the XF4F-3, We also have to believe that the addition of over 400lbs worth of engine (not counting intercoolers) and the larger propeller and military equipment would miraculously not affect the performance.