I do the same thing. I'm fluent in Spanish, but when I use Spanish words while speaking English, I certainly don't give them the full accent treatment! That would sound weird and probably a bit pretentious. I get the general sound and stress correct but don't do things like roll the r or overdo anything.
The funny thing is, the opposite is also true. When speaking Spanish, especially when I'm back in Spain, English words that are a normal part of Spanish speaking get a bit of a Spanish edge to them, though I'm sure they still sound authentically American to my Spanish friends. It's almost a little awkward not to. There's this big open vowel sound to Spanish and it would be harder to flatten everything back up again just for one word.
The funny thing is, the opposite is also true. When speaking Spanish, especially when I'm back in Spain, English words that are a normal part of Spanish speaking get a bit of a Spanish edge to them, though I'm sure they still sound authentically American to my Spanish friends. It's almost a little awkward not to. There's this big open vowel sound to Spanish and it would be harder to flatten everything back up again just for one word.