To piggy back off some of the previous tips...Few travelers have had items stolen from hotel rooms, however, theft from rooms does occur, so it still not a bad idea to give it a little consideration. Here are a few ideas for you to consider if you want additional security for your gear.
When you room safe is full, obviously you can ask to use one of the extra safe's at the front desk, but as you mentioned, it is inconvenient to run back and forth.
An additional idea is that you may want to bring your own portable safe with you. As strange as it sounds, I think you will find the following ideas interesting, while providing a unique solution to store your excess camera gear, laptop, or other valuables.
Portable Camera Safes
These come in a variety of sizes and shapes that can fit a little gear or a lot. They come in sizes ranging from a day bag to a gym bag. What makes them unique is that inside the material of the bag is a wire mesh that prevents the thief from cutting open your bag.
The more secure feature on these bags is that they feature a built in steel cable so you can lock the whole bag to a secure fixture in your hotel room, car, office, or any other location where you may need to leave your gear behind. While anything can be stolen if given the right tools, time, and determination, these bags will stop the majority of casual and opportunistic thefts, which are the bulk of thefts that travelers face.
Check out the videos on the various camera security products that are listed on the link below to give you an idea how they can protect your gear.
Camera Security Gear
Camera Security Straps
While much of the info on the above page is found on the other pages of the site, it provides an interesting looks at camera security straps that can be used to keep camera's safe from camera thieves overseas who have been known to cut regular camera strap from the rear when walking through busy crowds.
The below page also include some unique camera security info that might help too.
Camera Security Tips
Pickpocket Videos
This is a page devoted to pickpocket videos. While it may pertain mainly to wallets and women's purses, you will see by watching the videos how the same thefts can happen to camera gear when you set it down in crowded places just for a few mins..Most of these videos are for folks who travel over in Europe where bag thefts and pickpockets are a very real problem in major cities such as Barcelona, Rome, and related cities.
Hope the info increases your travel IQ so you can better protect your gear.