From the sound of it, this one has reached the point where the talks about "re-capping" come up. Electrolytic capacitors have a "shelf life" and when they do all kinds of things go "wonky". The electrolyte dries up, the capacitor becomes more of a resistor than a capacitor but, sometimes they DO still act like a capacitor but usually change value.... AND LEAK. When this "aging" happens bad caps in audio circuits and filter sections have a habit of turning "audio amps" into "oscillators" and SOMETIMES.... just BARELY into oscillators. THAT is when you will hear things like "motorboating"... which is what the sound you are describing is called.
When re-cap enters the discussion you will usually find two basic camps of opinion.
One is, "we know that electrolytic capacitors age and dry up.... save money, time and frustration....just do them all at once and be done with it!"
The other is, "if it ain't broke don't fix it. Trouble shoot the problem you are having and change out ONLY THE ONE or ONES that are bad and leave the others alone".
Camp #1 says that you save money and time because you just sit down and change them ONE AT A TIME being sure of VALUES and POLARITIES and NOW you have nice fresh caps in every single position and ASSUMING you have done an accurate job... your radio will stand a better chance of working for years and years down the road.
Camp #2 says that there are RISKS. Risks involving a poorly done job (mislocated caps, mis-polarized caps, soldering accidents.... things of that ilk!). They also often say that the caps don't fail as Camp #1 says they do and that some of the caps that you replace will STILL be good and ALSO say that it is possible that you may be installing lower quality caps that may fail soon or just not last as long.
Each must decide for themselves as I KNOW FOR A FACT that MANY MANY Camp #1'ers have done cap swaps with glorious results but I am certain that there have likely been caps installed backwards and in wrong locations (by the way, you generally ONLY do electrolytic caps. The ones in the little aluminum cans!).
Camp #2's main objections are 1) possibility of risk, and 2) changing out caps that are still good.
Speaking about "possibility of risk".... this one is most often covered by.... "GOT TO BE CAREFUL"!!!! Do them one at a time, taking careful note of the polarity as they COME OUT and put them back in the same way. And I mean... LITERALLY... .do them ONE AT A TIME is the safe way to go. Desolder, look at the polarization marks AS you pull the part out, put the next one in the same direction, solder it, trim the leads... on to the next one. Another risk centers around "cheap/inferior parts". Yes you can buy bargain caps from questionable sources ... and of questionable brands..... and they may indeed be "crap". If you stick to brand names that are known and good.... they DONT COST THAT MUCH MORE.... and will last for years. I have personally re-capped SSB radios..... taking about 54 caps total and spent right at $30 for NAME BRANDS from Mouser.... and the job was fine. IF YOU BUY CHEAP...... you may not be satisfied. Make a good choice here.
Speaking about "caps that are still good".... reasonable people could assume that, if ONE cap is bad.... since they are all the same rough age.... OTHERS COULD BE BAD AND HIDING FROM YOU.... waiting to fail!!!! Is it possible that some of them may be good still???? Certainly!!!!!! Is the expense in changing them ALL out so great that you should not consider doing it??? Well..... an SBE Console V is about 54 electrolytic caps. I bought the kit from KlondikeMike for under $30 bucks and did them all at once. Now I KNOW they are all good and all the same age. Could one of the new caps fail prematurely? Certainly!!!!!!! There is that chance with anything.
It is just "up to you" to make the decision as to whether it is worth it to just "wholesale change them all"....but it sounds like your baby is "at that point in time. That just sounds like "something wrong due to a drying up or dried up electrolytic cap" type of problem. It IS a tedious job... I grant you that. But if your soldering skills are good... and you have patience on tap... one could possibly do the job. If not... there are technicians that will do this. It will cost money... but they have experience and the skills to do it already!!!!
Sorry that this got kindof long... but just wanted you to know what I think you are up against and, if you talk to other people about it, this little post may help you know "ahead of time" what is going on.
Personally... I think your radio is worth it. Every bit of it.