Inside the DF300 brochure is a diagram where you can see the space needed from bracket to transom.
https://www.globalsuzuki.com/marine/lineup/df350a-325a-300b/pdf/DF350AMD_PI_web.pdf
Same should be available for your Yamaha so you may do a search for it.
The optional electronic steering of the DF350 will give a greater clearance between engine bracket and transom than a normal hydraulic steering ram. In the offer i got for them was written that electric steering is recommended and my guess is that it's for that reason.
Worst case would be the need to install a jack plate (fixed, manual or hydraulic) on the bracket to set the DF350 enough back to allow full tilt up. Consider that any set back plus the weight of the jack/setback plate will let sink the transom even deeper than the additional weight of the DF350.
I had twin Seastar/Dometic jack plates on my Venture 34 because the weight of the engine lowered the stern so much that lower units where too much submerged, but engines could tilt up totally. It was just the weight of the twin DF300AP and a 99 hull not designed for such high weight.
For your older hull it is likely that same/similar will happen so
i suggest you to test what the extra weight of the DF350 will do to boat level at rest. Calculate weight difference and then have a similar weight person standing on transom or sit on cowling to simulate extra weight. Take a photo before and after to have a reference stored.
The bracket you have is most likely a positive flotation bracket what will help with the weight, however i would check that first.
Too much weight on the transom can lead to water back flowing to the scuppers as they are under water and ventilation issues when going over the hump as the stern area sit too deep and plow to the water instead of hopping up.
I am considering to replace my twin F300 with twin DF350, but weight and price is considerable higher what steers me to install twin DF300AP instead, also because i know this engine very well.
Chris