A plywood top HD will have a decient sound but the exact same HD with a solid wood will sound different. Also over the long term plywood wont age out like solid wood so the sound wont change much. I dont think there has been any good (insterment) plywood around long enough to actually quantify the difference like solid wood insterments have been done. I make most of mine using quater inch birch plywood but I have made a few using various solid woods including cedar. Plywood allows you to make a decient HD at a cheaper price that a solid wood one. A plywood one will actually work fine for a lifetime for most people too. Theyre not nessarly an inferer HD either. Be suprised how many people have placed in the top 3 at the national championship contest at Winfield over the years using a plywood top HD too.
A fixed top hd can be made where the top isnt as mutch a structial part as many are. If the way one is made that requires the top to be a major structial member that top will be under compression between the pinblocks. Solid wood will expand and contract less WITH the gran than cross grain so for the greatest tuning stability you have to run the grain parallel to the strings. Wood has ts greaest stringth with the grain also. Plywood with equal ammounts of wood both ways expands and contracts about equal both directions.
The thickness of a Hd top affects the sound the same way as the top of any insterment does. With the same wood and all else being equal generally the thicker it is the less sound you will get. But due to the extremely high volume relitave to most other string insterments the difference between quarter and 3/8 isnt much of an issue. The thickness also affects the overall tone, generraly works out to thinner being a bit brighter.
The way a wood used in an insterment affects the sound is the same for any insterment. A hard dense wood such as maple will give a brighter sound and will reflect the highs real good. A soft less dense wood such as cedar will give a more mellow less bright sound. It will alsos asorb some of the highs more than maple acting as a reflector. A cedar top with a maple back will produce sort of a mellow sound with a reasonable brightness. One thats tottaly maple will give a real bright sound that is sorta edgy sounding to me. One that all cedar will sound a bit lacking in the highs.
From there on a Hd is nothing like any other insterment other than pianos as far as construction goes. String tensions can be anywhere from to to 3 times higher than say a guitar or MD. The total tension across a 15/14 2 string per course one can range from around 1200 pounds to over a ton! Where a string goes over a bridge or nut on say a md the strings produce a down force on them. On that md it is probally close to 10 pounds or so. The actual figure is a function of the string tensions and the break angle over that bridge or nut. On a typical Hd the down force on a bridge can be anywhere from 150 or so pounds to well over 300 PER BRIDGE! Now you know why its a real trick to make one under say 18 pounds that wont implode.
On mine the total tension is right at 1900 pounds. Every string is within 3 pounds of 38 pounds and the down force on the treb bridge is 315 pounds and on the base 345 pounds. The break angle on the base one is greater. Mine weigh 16 pounds give or take a pound depending on wood. I could easily get 2 or 3 more pounds out of one but I loose something I love doing that; all tuning pins that make tuning it soo easy and you dont have to mess with loop end strings either.
I notice you are expermenting with cedar. Ive made HDs with that as the top in thickness from just a hair over 1/8 all the way close to half inch. The way I do one the top dosent act as much of a structial member. The 1/8 inch top one has the best overall sound in my oppion. Cedar has a far higher with grain/cross grain differnatil expansion that most woods. In just about 19 inches, top to bottom the expanision across the grain with cedar is around 1/8 inch while with grain its far less. I havent actually measued it bt from the change in pitch of the strings its less than a 64th. As a result that 1/8 inch top develpes a bit of a concave buckle right under the bottom treb string after a few high humidity days. After a few days at a normal humidity it gets nice and level.
It probaly wouldnt do that if I didnt have the eges trapped in that trim band. The total thickness of the outside braces is right at an inch. The actual brace is 3/4 wood and that trim band is usally a quarter inch thick. The trim band sticks up high enough to hide the edge of the plywood tops and I dont changg that for solid wood tops. Far easier to do them all the same other than the additional work to get a solid wood top than a peice of plywood.