I realize that regardless of what I put on the rear - 4.00 or 4.50 - that a modification of the swing arm will be required.

The outside diameter of the 4.00 is 26.42".
The outside diameter of the 4.50 is 27.2.0".

I am okay cutting away at some of the swing arm to fit the 4.00 tire. But, it seems like I would have to cut away too much to fit the 4.50 tire.

I suppose if I go for the 4.5, instead of cutting away the swing arm, I could use the swing arm extensions that Ryca makes.

Badwolf is correct......the tires you are looking at will work fine if you are riding for style, and not too concerned about performance.  The tires are "old school" in tread design and carcass shape.

Here is the thread for Cafe tire discussion.....the bottom line is folks should not be mounting the 130/70-18 tire on a 18x2.50 rim as the tire is designed for a wider rim - if you want to run a tire that size the rim should be a 18x3.50.  The following thread has a chart to show what width rim you should be using for a tire width/profile.
http://suzukisavage.com/cgi-bin/YaBB.pl?num=1435340395

With your choice of a very tall rear tire - you may also run into a problem with the clearance for the bottom of the seat/fender bodywork.  When your shocks bottom out - you are likely going to suffer from the tire hitting the tail light.  Depending on what shocks you use, you may need to install spacers to limit the amount of travel if you want to keep your tail light.  (13.5" shock length is about the maximum you can run before you start having belt tension issues, as the swing arm gets to be at too steep of an angle with longer shocks....and the belt can rub on the swing arm.....and this problem is even worse if you were going to use a chain).

The size/weight of the tires does affect the way the bike handles.  The more mass and the larger the circle - the more the bike will resist changes in direction.  If you like going in straight lines stability is good - but if you like a a bike that can be flicked from one curve into the next, the ride will feel stiff and rigid.....and the clip on handlebars are narrow and don't give you a lot of leverage.

In the stock cruiser form with the shallow fork angle you can feel the front wheel "flop" from one side to the other when you steer - when you drop the forks and raise the rear the bike for the Cafe' the flop goes away and the bike turns more like a standard motorcycle.  Adding the mass of the 4.00-18 tires on both ends will change the stability and require you to put more pressure on the bars to initiate the turn....and more pressure to come out of the turn.

As mentioned earlier - the Shinko 270 tire are a bit of a mismatch for a Cafe' bike.  The tire design is from an era when bikes had rigid frames and very limited lean angles - it is a tire that can provide a vintage look and vintage handling characteristics.  The 4.00-18 will most likely fit on the back with the swing arm modification and you may need to limit the shock travel - I am not sure about it fitting on the front...measure the width between the fork legs to confirm there is clearance.....I am not sure how wide the sidewalls are on a 4.00-18.  Check the RYCA customer bike build photos - I know some folks have used the vintage looking tires on their builds.

I will support your choice and the "look" that you are going for - however the bike will be more fun to ride with a more modern tire choice and you may ride it more often.

 

So, if I went away from the vintage look and wanted something a little more performance oriented - not hardcore performance but something for more general riding and good handling - what say you on something like this:

Dunlop D404
front: 100/90-18
rear: 110/90-18

Also, with the overall diameter of that rear tire being 25.51", I may not even need to do the swing arm mod either.

https://www.dunlopmotorcycletires.com/tire-line/d404/

Thanks again for all the advice!