Your approach is not an unusual one, engine brakes to measure horsepower usually make use of such a method, but they use much bigger water barrels. To answer your questions:
"Can I just fill a tub of water, and divide the output exhaust into 4/5 tubes, take them through a tank of water?"
A: Yes you can, but the heat exchange between the water and the exhaust gas is not known, so you don't know the diameter or lenght of pipe needed for the desired temperature drop. The only thing known is that the cooling gets worse when the difference in temperature between water/exhaust gas gets lower. That happens when the water heats up after you have tested for a while. Using more tubes gives better cooling.
What's the amount of water that'd be required for the setup to be able to give that much heat reduction, for ~ an hour?
A: That heavily depends on the efficiency of the pipes regarding heat exchange. More pipes is better, more surface is better(bigger or folded pipes), thinner wall thickness is better, materials with lower heat resistance is better(like copper or else aluminum).
What sort of geometry should I build to not have much back-pressure on the gas flow.
A: I'd suggest a cooling spiral within your barrel, that will give the least resistance to the gas flow. Sharp turns in your piping make things worse.
What'll likely be the best material to build these pipes?
A: Copper is an excellent heat exchanger and still afforable. Aluminum is also good at it, and even less expensive. You can buy those crumpled up, thin walled aluminum pipes for aircon units and such. I'd recommend these with a 50mm/2in diameter:
You just want to create as much surface as possible, as thin as possible to reduce the total heat resistance. Crumpled up pipes create more surface, adding more pipes adds more surface. The more crumpled up, the better. It's just like air filters. The crumpliness of the pipes does add a tiny bit of resistance to gas flow, but you won't notice it.
What's the best direction/references/designs to look into for design such, water bath/non-circulating type heat exchangers?
A: I wouldn't know, but I think you've now got enough information to proceed.
Maybe take a look at instructables.com for some inspiration if you get stuck.
The needed amount of water will depend on the airflow from the exhaust.
Assuming a 2 litre four stroke engine revving at WOT at 4000rpm and 90% volumetric efficiency, you'd get an inlet volume airflow of:
$Volume flow = 2*(1/2)*(4000/60)*0.9 = 0.06 m3/s$ or about 127CFM.
The ambient temperature you give is 23 degrees. Air at that temperature has a density of about 1.185kg/m3 at 1 bar. Assuming an absolute manifoldpressure of 1 bar at WOT, that would translate in a mass airflow of:
Air has a specific heat of 287 J/kgK, so every degree temperature drop per kilogram gives you 287 Joules of heat energy. We're not dealing with dry air, but with exhaust gas which also containt about 1/15 part fuel which has different properties. So let's take 300J/kgK for specific heat to compensate that.
A temperature drop of 90 degrees C (150-60) over our mass flow thus yields a cooling power of:
That's nearly exactly the power that the average watercooker has. You can imagine how fast the water will be heated up. We can calculate that. Water has a specific heat of about 4200J/kgK. So let's say your barrel contains 20Litre(thus ~20kg) of water, then our 1920Watts of power will heat up the water
$dt/s=1920/(4200*20)=0.023 K/sec$ or about 1 degree every 44 seconds.
The surrounding air also cools down the barrel in turn, but let's ignore that for the sake of simplicity here.
That means that our 20L of water will boil in 56 minutes, given that the cooling will be constant. But it won't, it will cool less and less the warmer it gets.
And if you want an exhaust gas temperature of 60 degrees, you obviously have to maintain water temperature (a lot) lower than that. Let's say it can't rise above 45 degrees. That means that the water can rise 22 degrees above ambient, which gives us 16 minutes of cooling before we reach a water temperature of 45 degrees.
NB: this is a calculation that takes a lot of assumptions, and your mileage will vary wildly if the operating conditions of the engine are different from what I assumed. Fill in your own engine properties to get an idea of your situation.
My advice: create some margin, i'd recommend to find an old 200L oil barrel, and use 5 50mm aluminium hoses of about 3 metre, as shown in the picture. Create a little spacing between the hoses for water to flow between, to maximise cooling efficiency. Make a spiral of the hoses in the barrel to keep air restriction at a minimum. Observe the water temperature in the barrel to get an idea how fast it will rise to a level that it won't cool anymore. Preferably make the air flow upwards in the spiral. Thermo syphon working will keep the water circulating in the barrel for maximum cooling efficiency. You can vary the hose length to maintain your 60 degrees air output as the water temperature rises.