With the relative age of your other accounts applying for and taking advantage of one or two of these offers should not cause any damage to your credit profile. There may be some slight initial damage for the new accounts but that would fade and recover in 6 months to a years time. Just be careful of any annual fees that may be associated with the offers. It is OK to open and close a card if it suits your purpose to do that but my opinion is that I look for cards that will serve my purpose long term with rewards or interest rates and the opening offers are just an added bonus.
And since you mentioned mortgage shopping, the usual advice is to not have new account or derogatory activity for a year before applying. It is not an automatic denial reason but as on the old TV show the underwriter will say "Lucy you have some splaining to do" 