Example 1 contains the correct reading of this rule.

As pointed out by Ernir, the Magic Item Compendium contains updated rules and clarifications for the creation of magic items.

Page number 233 of the Magic Item Compendium covers this case and states that:

In most cases, if the item is one that occupies a body slot, the cost of adding any additional ability to that item is 1-1/2 times the value of the added power (or the value of the added power plus 1/2 the value of the existing item, if the added power normally costs more than the existing item). For example, if a character adds the power to confer feather fall to her ring of jumping, the cost of adding this ability is 3,300 gp, the same as for creating a ring of feather falling × 1-1/2. On the other hand, if she were adding the power of a ring of force shield to that ring of jumping, the cost of adding the ability would be 9,750 gp (8,500 gp for the ring of force shield plus half of 2,500 gp, the price of a ring of jumping).

It is also worth noting that the Magic Item Compendium updates the cost of Multiple Different Abilities to be 1.5x instead of 2x.

There's a factor you missed out on: the square-cube law. As Wikipedia describes it:

When an object undergoes a proportional increase in size, its new surface area is proportional to the square of the multiplier and its new volume is proportional to the cube of the multiplier.

Let's consider the implications of this for a moment with a cube of water: it will be one centimeter along each side, and will weigh one gram.

By your math, if you want a cube of water that's ten times bigger, you also just times the weight by 10, for a final weight of 10 grams. But that's just ten times the water, and I think we'll agree there's a big difference between ten spiders and a ten times taller spider. What you probably mean by 'ten times bigger' is a cube that's ten times bigger along each dimension. That gives us a 10 × 10 × 10 cm cube of water.

We'll see what the square-cube law has to say about increasing each dimension by 10, using that 10 as our size multiplier:

• The surface of one side goes from 1 square centimetre to 100 square centimetres. That means the cube's total surface area goes from 6cm² to 600cm². This surface area got increased by the square of the multiplier, 100.
• The volume of the cube goes from 1cm³ to 1,000cm³ (10 × 10 × 10cm). This volume got increased by the cube of the multiplier, 1000.
• Since the weight of water is 1 gram per cubic centimetre, this now weighs 1,000g, or a kilogram.

Applying this to a spider

Let's assume the spider's anatomy remains identical as it gets proportionately bigger, and that an increase in volume leads to an exactly proportional increase in weight. (In reality, an enormous spider would need to have much sturdier anatomy, better breathing systems, and other stuff in order to be able to avoid suffocating and its own exoskeleton caving in on it, but they might not know that. Let's assume imaginary radiation magic is helping here.)

Original: 5.3 ounces at 12 inches.

Multiplication factor: 10, for going from 1 foot across to 10 feet across.

New weight: 5.3 × 10³ = 5.3 × 1,000 = 5,300 ounces = 331 pounds.

This is about the weight of a very young elephant (they're ~200 pounds when born). The large entry suggests creatures this big should weigh at least 500 pounds, so either this is spider is a near-the-mark outlier, or large spiders have actually developed much sturdier, denser, stronger anatomy for their size and thus weigh a lot more. Imagining an enormous spider with more elephantine body/leg proportions is awesome and terrifying for me.

Enjoy your new spider!