Are there any records from the Constitutional Convention that establish why the District of Columbia was denied voting representation in the Senate and the House? Was there even any expression of concern that in DC there would be taxation without representation?
Such concern likely existed, and there is evidence of some cursory discussion to that effect during the proceedings of the Continental Congress. The rationale for creating a federal district with sole jurisdiction of the Congress was probably laid out best (among the surviving documents) by James Madison:
The indispensable necessity of complete authority at the seat of government, carries its own evidence with it. It is a power exercised by every legislature of the Union, I might say of the world, by virtue of its general supremacy. Without it, not only the public authority might be insulted and its proceedings interrupted with impunity; but a dependence of the members of the general government on the State comprehending the seat of the government, for protection in the exercise of their duty, might bring on the national councils an imputation of awe or influence, equally dishonorable to the government and dissatisfactory to the other members of the Confederacy. This consideration has the more weight, as the gradual accumulation of public improvements at the stationary residence of the government would be both too great a public pledge to be left in the hands of a single State, and would create so many obstacles to a removal of the government, as still further to abridge its necessary independence.1
The issue of representation is mentioned a little bit further in the document, and is basically pointing out that the importance of federal holdings to the nation runs counter to resident governance.
Nor would it be proper for the places on which the security of the entire Union may depend, to be in any degree dependent on a particular member of it. All objections and scruples are here also obviated, by requiring the concurrence of the States concerned, in every such establishment.2
While Madison is referring most directly to military installations, the inference is likely one that can be extended to the seat of government. To understand the connection between security and seat of government, the context of the decision-making process about locating the proceedings of the Congress is important. The bulk of the debate took place around October of 1783, and was in part precipitated by Pennsylvania Mutiny of 1783. Under the Articles of Confederacy, the Congress relied on the Pennsylvania militia to provide security. The Pennsylvania Council chose not to do so, and allowed an angry mob to march on the Congressional proceedings. Also, the role of being able to come to a compromise on where the seat of government should be located was likely a big part - on October 6, 1783 motions to house the Congress in each of the 13 states were voted down.3
About the only mention I can find from around this period is again from Madison, this time in a letter to Edmund Randolph dated September 20, 1783:
Among other subjects which divide Congress, their constitutional authority, touching such an establishment in time of peace is one. Another still more puzzling is the precise jurisdiction proper for Congress with the limits of their permanent seat. As these points may possibly remain undecided till November, I mention them particularly that your aid may be prepared.4
Outside of that, it doesn't appear to have been one of the considerations. Not only did the Congress have a much more pragmatic outlook on the subject, the area under consideration with only a few square miles. Wilhelmus Bogart Bryan summed up the record of discussions regarding the jurisdiction for the federal district in writing about the response to recommendations presented to the Congress for its establishment:
This report was referred to the committee of the whole, but there is no record that any further action was taken. In the papers of the continental congress there are two documents evidently intended as amendments, but their place and purpose are not indicated in any way. In one of the papers the principle is laid down that such a district "ought to be entirely exempted from the authority of the state ceding the same, and the organization and administration of the powers of government within the said district concentrated between Congress and the inhabitants thereof." The other paper prescribes that the state or states ceding the territory "should give up all jurisdiction whatsoever ... that the appointment of judges and the executive power within the said territory shall vest in Congress; ... that the citizens should enjoy the privilege of trial by jury and being governed by laws made by representatives of their own election." 5
Beyond that, there doesn't appear to me anything other than a general consensus that Congressional authority over the District, as it was incorporated without much modification as the beginning of Article I, Section 8 of the Constitution:
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States...
1 Madison, James. The Federalist No. 43, p. online
3 United States Continental Congress. Journals of the American congress: from 1774 to 1788 - Volume 4, p. 283-6
4 Madison, James. The Papers of James Madison, Volume 1, p. 573
5 Bryan, Wilhelmus Bogart. A History of the National Capital, Volume 1, p. 15