What size is suggested for a larger contact surface tire?
Use the size specified by the bike manufacturer. If it could have had a bigger/fatter tire they would have told you so in the owners manual.
It is similar to asking if you can put chevy big block pistons in the motor to increase the displacement and power of the bike. There is far more to it than simply the piston itself.
Since neither you nor you wife, (nor many of the forum members, for that matter, (present company excepted)), know enough about tire technology or rim design, to re-engineer the bike configuration in a favorable way, stick with the stock sizes, or find another bike that has the tires you desire.
It is generally accepted that you "can" fit tubeless tires onto a tube type rim. You, of course, must use a tube, which lowers the effective speed rating of the tire. You also have to find someone experienced with doing this, as the tubeless tire doesn't "automatically seat properly on a tube type rim like they do on a tubeless rim. One has to cajole the tire bead to seat evenly all around the circumference, or the bike will wobble like the tires are out of balance (because the tire tread doesn't spin true). The bead seating issue becomes more difficult as tires are fitted that require a wider rim than what is currently on the vehicle.
Tire compounds harden with age and this diminishes traction, certainly on paved roads. A new tire will have more resilient rubber and provide better traction. Some tires are made with softer rubber than others, even within the brand selection. Unless, your new selected tire has an old date code, it should provide better grip than an old tire you are currently using.
There has also been some speculation that Chinese tire manufacturers make tires that last longer on unimproved roads. These roads wear tires faster, so the manufacturer selects a hard compound for longer life. When these tires are applied to improved or paved roads, they last a really long time but do not provide the grip of a softer tire.
Then there is the issue of the road composition you will be driving on. It is the other half the traction equation. What aggregate is in the road you will travel? Some local areas use an aggregate that is coarser than others. Crushed coral or crushed rock has far more grip potential than stream washed/polished rounded stones. The aggregate filler is selected by price and minimum hauling distance. Not by it's traction abilities.
FYI, if you simply want a larger contact patch, then lower your tire air pressures. But, I think you will find that brings other unwanted tire and handling and tractive issues. However, this is a common technique for improving traction on sand.
