Without some sort of unobtanium it will be difficult to substantially increase the diameter of an earth-like wold without also substantially increasing its surface gravity.
If you replace most/all of the iron in the core with lighter materials like silicates and magnesium, you might be able to reduce the density of the core by ~50%. But as the core only makes up about 10% by volume, this would only reduce the average density by around 5% - assuming this could still produce a planet with a crust still containing substantial amounts of iron and other heavy elements as found on the earth. You could possibly do a little bit better by changing the ratio of silicon to other elements, but probably only a couple more percent difference in density. Voids and porosity won't work - at the sort of pressures you find in the core there are no voids. You could go a bit more extreme by replacing substantial amounts of silicon and similar elements with water, carbon and other lighter materials. This could reduce density substantially, but now the crust (and the tectonics) is definitely not going to resemble that of earth (maybe substantial engineering by a super-civilization could get you a reasonable approximation - but it would not form 'naturally').
So assuming a density 7-10% less than that of the earth, surface gravity scales as density $\times$ radius2. So if you allowed for surface gravity to be maybe 10% higher than earth's (is that similar enough?) - you could get away with approximately 10% greater radius. This would provide you with ~30% more surface area. If you want to retain ~1g then you are probably limited to radius increase of no more than 4-5% without weird global engineering.
Spinning faster won't help reduce surface gravity unless you spin ridiculously fast - 20 minute days anyone?
Increasing the tilt angle would make the climate more extreme (possibly much more extreme). And as a larger world would likely have more extreme weather anyway (more space for thermal gradients etc to develop), you would likely get a pretty stormy climate with much higher average wind speed. Perhaps that will help you get what you want - a slightly bigger planet with a slightly higher frequency of horrible weather would indeed be harder to explore.
As an added note - re-positioning the continents can also make things more difficult for exploration. If the Pacific was narrowed by 30% then the Atlantic could be widened by ~50% (without significantly altering the shape of the continents). This would have made it harder/impossible for Columbus etc. to have 'discovered' the new world (which could have led to at least a century delay till it was found by Europeans).