The statements made by the Toyota specialist shop are new to me.
I am not a mechanic, so I don't want to jump on what a mechanic, who had the vehicle right in front of them stated.
The point that I am making is that all the trolling on several forums that I have been doing has not gotten me anything on the 1MZFE motor having valve issues.
There are LOTS of these motors out there......as they used the 1MZFE motor in camry and also many Lexus vehicles.
There are LOTS of these motors that are both older and also with double the mileage on them that you have.
I have a 2003 Sienna, which has the VVT (Variable Valve Timing).
I did read the procedure for "adjusting" the valves......which is installing the shims as you mention has been done.
I would not attempt it myself, as it is involved.
There is a good amount of tollerance in valve adjustment.......before you will be left by the roadside.
A picture of the front valvetrain on my 2003......The rear camshaft has the VVT....the fat part on the gear on the top right......non-VVT will look pretty much the same, only with the fat gear in the picture looking like the bottom gear.
Being slightly out of adjustment is not going to make your cam shafts suddenly fail (you have 4....2 per bank of cylinders, 1 for each intake bank of valves, another for each exhaust bank of valves). If the valve adjustment would impact the cam shafts......I would expect there would be wear on the cam lobes....the part that contacts the valve shaft...parts.
Your mechanic would have noticed this.
Another sound that is very similar.....and also located very close to the same spot.....would be the fuel injectors.
Each fuel injector has a plunger that goes up and down with each time it squirts fuel.
Fuel injectors also make a tapping noise.
A mechanic should be able to determine if the sound is from a fuel injector or valves, but I would not know from just sticking my head under the hood.
I would make sure that the timing belt has been changed on the proper schedule (I think it is every 90K miles, as it is for my 2003).
One option, if you are not confident in your vehicle, is to rent a vehicle for the trip.
It costs, but it is much cheaper than dumping a pile of money to get a new vehicle because of a concern over a long trip.
One thing that I like to do before a long trip (I take mine on a youth mission work trip each year) is to take it to a trusted shop and have a "safety inspection" done.
This will cost around $100 or so as this is not just a quickie look......they spend some time with your vehicle.
I would be more concerned about routine wear items, like tie rod ends, brakes, tires, etc
Most of these things (like tie rod ends and ball joints) don't suddenly fail, they fade away.......and only suddenly fail if left go long after a mechanic would have caught it for you.